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http://www.hpcsoft.com/products/MathSoL/specialFunction/LegendreFunction.pdf  




Table: First-Order Legendre Functions  (Legendre Orthogonal Polynomial Functions)-


x P2(x) P3(x) P4(x)
0 -0.5 0 0.375
0.01 -0.49985 -0.0149975 0.37462504375
0.02 -0.4994 -0.02998 0.3735007
0.03 -0.49865 -0.0449325 0.37162854375
0.04 -0.4976 -0.05984 0.3690112
0.05 -0.49625 -0.0746875 0.36565234375
0.06 -0.4946 -0.08946 0.3615567
0.07 -0.49265 -0.1041425 0.35673004375
0.08 -0.4904 -0.11872 0.3511792
0.09 -0.48785 -0.1331775 0.34491204375
0.1 -0.485 -0.1475 0.3379375
0.11 -0.48185 -0.1616725 0.33026554375
0.12 -0.4784 -0.17568 0.3219072
0.13 -0.47465 -0.1895075 0.31287454375
0.14 -0.4706 -0.20314 0.3031807
0.15 -0.46625 -0.2165625 0.29283984375
0.16 -0.4616 -0.22976 0.2818672
0.17 -0.45665 -0.2427175 0.27027904375
0.18 -0.4514 -0.25542 0.2580927
0.19 -0.44585 -0.2678525 0.24532654375
0.2 -0.44 -0.28 0.232
0.21 -0.43385 -0.2918475 0.21813354375
0.22 -0.4274 -0.30338 0.2037487
0.23 -0.42065 -0.3145825 0.18886804375
0.24 -0.4136 -0.32544 0.1735152
0.25 -0.40625 -0.3359375 0.15771484375
0.26 -0.3986 -0.34606 0.1414927
0.27 -0.39065 -0.3557925 0.12487554375
0.28 -0.3824 -0.36512 0.1078912
0.29 -0.37385 -0.3740275 0.09056854375
0.3 -0.365 -0.3825 0.0729375
0.31 -0.35585 -0.3905225 0.05502904375
0.32 -0.3464 -0.39808 0.0368752
0.33 -0.33665 -0.4051575 0.01850904375
0.34 -0.3266 -0.41174 -0.0000353
0.35 -0.31625 -0.4178125 -0.01872265625
0.36 -0.3056 -0.42336 -0.0375168
0.37 -0.29465 -0.4283675 -0.05638045625
0.38 -0.2834 -0.43282 -0.0752753
0.39 -0.27185 -0.4367025 -0.09416195625
0.4 -0.26 -0.44 -0.113
0.41 -0.24785 -0.4426975 -0.13174795625
0.42 -0.2354 -0.44478 -0.1503633
0.43 -0.22265 -0.4462325 -0.16880245625
0.44 -0.2096 -0.44704 -0.1870208
0.45 -0.19625 -0.4471875 -0.20497265625
0.46 -0.1826 -0.44666 -0.2226113
0.47 -0.16865 -0.4454425 -0.23988895625
0.48 -0.1544 -0.44352 -0.2567568
0.49 -0.13985 -0.4408775 -0.27316495625
0.5 -0.125 -0.4375 -0.2890625
0.51 -0.10985 -0.4333725 -0.30439745625
0.52 -0.0944 -0.42848 -0.3191168
0.53 -0.07865 -0.4228075 -0.33316645625
0.54 -0.0626 -0.41634 -0.3464913
0.55 -0.04625 -0.4090625 -0.35903515625
0.56 -0.0296 -0.40096 -0.3707408
0.57 -0.01265 -0.3920175 -0.38154995625
0.58 0.0046 -0.38222 -0.3914033
0.59 0.02215 -0.3715525 -0.40024045625
0.6 0.04 -0.36 -0.408
0.61 0.05815 -0.3475475 -0.41461945625
0.62 0.0766 -0.33418 -0.4200353
0.63 0.09535 -0.3198825 -0.42418295625
0.64 0.1144 -0.30464 -0.4269968
0.65 0.13375 -0.2884375 -0.42841015625
0.66 0.1534 -0.27126 -0.4283553
0.67 0.17335 -0.2530925 -0.42676345625
0.68 0.1936 -0.23392 -0.4235648
0.69 0.21415 -0.2137275 -0.41868845625
0.7 0.235 -0.1925 -0.4120625
0.71 0.25615 -0.1702225 -0.40361395625
0.72 0.2776 -0.14688 -0.3932688
0.73 0.29935 -0.1224575 -0.38095195625
0.74 0.3214 -0.09694 -0.3665873
0.75 0.34375 -0.0703125 -0.35009765625
0.76 0.3664 -0.04256 -0.3314048
0.77 0.38935 -0.0136675 -0.31042945625
0.78 0.4126 0.01638 -0.2870913
0.79 0.43615 0.0475975 -0.26130895625
0.8 0.46 0.08 -0.233
0.81 0.48415 0.1136025 -0.20208095625
0.82 0.5086 0.14842 -0.1684673
0.83 0.53335 0.1844675 -0.13207345625
0.84 0.5584 0.22176 -0.0928128
0.85 0.58375 0.2603125 -0.05059765625
0.86 0.6094 0.30014 -0.0053393
0.87 0.63535 0.3412575 0.04305204375
0.88 0.6616 0.38368 0.0946672
0.89 0.68815 0.4274225 0.14959804375
0.9 0.715 0.4725 0.2079375
0.91 0.74215 0.5189275 0.26977954375
0.92 0.7696 0.56672 0.3352192
0.93 0.79735 0.6158925 0.40435254375
0.94 0.8254 0.66646 0.4772767
0.95 0.85375 0.7184375 0.55408984375
0.96 0.8824 0.77184 0.6348912
0.97 0.91135 0.8266825 0.71978104375
0.98 0.9406 0.88298 0.8088607
0.99 0.97015 0.9407475 0.90223254375
1 1 1 1

x P5(x) P6(x) P7(x)
0 0 -0.3125 0
0.01 0.018741250788 -0.311843946861 -0.021855316831
0.02 0.0374300252 -0.309878149076 -0.043592638566
0.03 0.056013941362 -0.30660968635 -0.065094489407
0.04 0.0744408064 -0.302050340864 -0.086244430807
0.05 0.092658710938 -0.296216571289 -0.106927576709
0.06 0.1106161236 -0.289129476404 -0.127031104742
0.07 0.128261985512 -0.280814748318 -0.146444762006
0.08 0.1455458048 -0.271302615296 -0.165061364101
0.09 0.162417751088 -0.260627774196 -0.182777286048
0.1 0.17882875 -0.2488293125 -0.19949294375
0.11 0.194730577662 -0.235950619963 -0.215113264646
0.12 0.2100759552 -0.222039289856 -0.229548146196
0.13 0.224818643238 -0.20714700982 -0.24271290086
0.14 0.2389135364 -0.191329442324 -0.254528686204
0.15 0.252316757812 -0.174646094727 -0.264922918799
0.16 0.2649857536 -0.157160178944 -0.273829670543
0.17 0.276879387388 -0.138938460723 -0.281190046075
0.18 0.2879580348 -0.120051098516 -0.286952539904
0.19 0.298183677962 -0.100571471968 -0.291073371934
0.2 0.30752 -0.080576 -0.2935168
0.21 0.315932479538 -0.060143948503 -0.294255408091
0.22 0.3233884852 -0.039357227636 -0.293270368891
0.23 0.329857370112 -0.018300178728 -0.290551679296
0.24 0.3353105664 0.002940649216 -0.286098367549
0.25 0.339721679688 0.024276733398 -0.279918670654
0.26 0.3430665836 0.045617821516 -0.272030180697
0.27 0.345323514263 0.066872186435 -0.262459958741
0.28 0.3464731648 0.087946891264 -0.251244614943
0.29 0.346498779838 0.108748064822 -0.238430353521
0.3 0.34538625 0.1291811875 -0.22407298125
0.31 0.343124206413 0.149151387519 -0.20823787811
0.32 0.3397041152 0.168563747584 -0.19099992875
0.33 0.335120371988 0.187323621927 -0.172443413408
0.34 0.3293703964 0.205336963756 -0.152661856943
0.35 0.322454726563 0.222510663086 -0.131757834619
0.36 0.3143771136 0.238752894976 -0.109842733302
0.37 0.305144616138 0.253973478155 -0.0870364667
0.38 0.2947676948 0.268084244044 -0.063467143318
0.39 0.283260306713 0.280999416174 -0.039270685753
0.4 0.27064 0.292636 -0.0145904
0.41 0.256928008288 0.302914183104 0.010423506603
0.42 0.2421493452 0.311757745804 0.035614460127
0.43 0.226332898863 0.319094482145 0.060820108859
0.44 0.2095115264 0.324856631296 0.085872967516
0.45 0.191722148437 0.328981319336 0.110601118213
0.46 0.1730058436 0.331411011436 0.134828969541
0.47 0.153407943012 0.332093974437 0.158378075105
0.48 0.1329781248 0.330984749824 0.181068012872
0.49 0.111770508588 0.328044637089 0.202717326676
0.5 0.08984375 0.3232421875 0.22314453125
0.51 0.067261135162 0.316553708252 0.242169182105
0.52 0.0440906752 0.307963777024 0.25961301164
0.53 0.020405200737 0.297465766925 0.275301132813
0.54 -0.0037175436 0.285062381836 0.289063311727
0.55 -0.028194804688 0.270766202148 0.300735310498
0.56 -0.0529387264 0.254600240896 0.310160301732
0.57 -0.077856255112 0.236598510282 0.317190355981
0.58 -0.1028490452 0.216806598604 0.321688003525
0.59 -0.127813364538 0.195282257567 0.323527871823
0.6 -0.15264 0.172096 0.3225984
0.61 -0.177214162962 0.147331707962 0.318803631702
0.62 -0.2014153948 0.121087251244 0.31206508769
0.63 -0.225117472388 0.093475116267 0.302323719508
0.64 -0.2481883136 0.064623045376 0.28954194559
0.65 -0.270489882812 0.034674686523 0.273705771143
0.66 -0.2918780964 0.003790253356 0.254826993171
0.67 -0.312202728237 -0.02785280431 0.232945491983
0.68 -0.3313073152 -0.060059119616 0.208131610542
0.69 -0.349029062662 -0.092614717393 0.180488622994
0.7 -0.36519875 -0.1252863125 0.15015529375
0.71 -0.379640636088 -0.157820597766 0.11730852845
0.72 -0.3921723648 -0.189943521536 0.082166118175
0.73 -0.402604870513 -0.221359554828 0.044989578252
0.74 -0.4107422836 -0.251750948084 0.006087083005
0.75 -0.416381835938 -0.280776977539 -0.034183502197
0.76 -0.4193137664 -0.308073181184 -0.075411490243
0.77 -0.419321226363 -0.33325058434 -0.117130141581
0.78 -0.4161801852 -0.355894914836 -0.158813332177
0.79 -0.409659335788 -0.375565807791 -0.199872118755
0.8 -0.39952 -0.391796 -0.2396512
0.81 -0.385516034212 -0.404090513931 -0.277425272345
0.82 -0.3673937348 -0.411925831316 -0.312395279004
0.83 -0.344891743638 -0.41474905636 -0.3436845509
0.84 -0.3177409536 -0.411977068544 -0.370334838129
0.85 -0.285664414062 -0.402995665039 -0.391302230615
0.86 -0.2483772364 -0.387158692724 -0.405452966608
0.87 -0.205586499487 -0.363787169808 -0.411559127657
0.88 -0.1569911552 -0.332168397056 -0.408294218732
0.89 -0.102281933912 -0.291555058626 -0.394228632118
0.9 -0.04114125 -0.2411643125 -0.36782499375
0.91 0.026756892663 -0.180176870533 -0.327433390626
0.92 0.1017469952 -0.107736068096 -0.271286477947
0.93 0.184172158238 -0.02294692333 -0.197494464641
0.94 0.2743841764 0.075124813996 -0.10403997591
0.95 0.372743632812 0.187453624023 0.011227208545
0.96 0.4796199936 0.315055188736 0.150595541975
0.97 0.595391702387 0.458987374287 0.316497225063
0.98 0.7204462748 0.620351223724 0.511513848778
0.99 0.855180392962 0.800291960102 0.738382166962
1 1 1 1

x P8(x) P9(x) P10(x)
0 0.2734375 0 -0.24609375
0.01 0.272453666312 0.024573295325 -0.24474140707
0.02 0.269508656495 0.048930450193 -0.240698433738
0.03 0.264621910527 0.072857009959 -0.234006869907
0.04 0.257825715945 0.096141881478 -0.224736361359
0.05 0.249165039561 0.118578988589 -0.212983531689
0.06 0.23869729257 0.139968897373 -0.198871109012
0.07 0.226492029765 0.160120401274 -0.182546813419
0.08 0.212630583769 0.178852056304 -0.164182012834
0.09 0.197205635401 0.195993656727 -0.14397015656
0.1 0.180320721484 0.211387641836 -0.122124997387
0.11 0.162089681634 0.224890424647 -0.09887861472
0.12 0.14263604573 0.236373633651 -0.074479252684
0.13 0.122092364008 0.245725259038 -0.049188988625
0.14 0.100599481905 0.252850695174 -0.023281248798
0.15 0.078305761974 0.257673671491 0.002961810599
0.16 0.055366255413 0.260137064341 0.029252037688
0.17 0.031941825946 0.260203582842 0.055298113907
0.18 0.008198228984 0.257856322214 0.080808456112
0.19 -0.015694850779 0.253099178606 0.105494169178
0.2 -0.0395648 0.24595712 0.1290720256
0.21 -0.063237111996 0.236476308323 0.151267447817
0.22 -0.086536452986 0.224724068551 0.171817468342
0.23 -0.10928775531 0.210788701234 0.190473642218
0.24 -0.131317333461 0.194779135542 0.207004885922
0.25 -0.152454018593 0.176824420691 0.221200216562
0.26 -0.172530306916 0.157073054334 0.232871365065
0.27 -0.191383517243 0.135692147309 0.241855237089
0.28 -0.208856952701 0.112866424965 0.248016195512
0.29 -0.224801061446 0.088797066138 0.251248138743
0.3 -0.239074591016 0.063700381758 0.251476349516
0.31 -0.251545730731 0.037806335992 0.248659089557
0.32 -0.262093236386 0.011356913785 0.242788916328
0.33 -0.270607531233 -0.015395660328 0.233893699084
0.34 -0.276991777087 -0.042190846225 0.222037312717
0.35 -0.281162909169 -0.068761848067 0.207319989288
0.36 -0.283052628083 -0.094837801939 0.189878308748
0.37 -0.282608342159 -0.120146082064 0.169884812252
0.38 -0.279794053152 -0.144414715203 0.147547223461
0.39 -0.274591178109 -0.167374891649 0.123107265587
0.4 -0.2669993 -0.18876356 0.0968390644
0.41 -0.257036839515 -0.208326091583 0.069047130221
0.42 -0.244741640228 -0.225818999139 0.040063914893
0.43 -0.230171459109 -0.241012692996 0.010246943021
0.44 -0.213404354183 -0.253694256602 -0.020024479755
0.45 -0.194538960927 -0.263670221866 -0.050352974861
0.46 -0.173694648777 -0.270769323307 -0.080327204671
0.47 -0.151011548946 -0.274845208547 -0.109526377181
0.48 -0.126650444511 -0.275779081132 -0.137525121932
0.49 -0.100792513569 -0.27348225016 -0.163898712687
0.5 -0.073638916016 -0.26789855957 -0.188228607178
0.51 -0.045410214332 -0.259006668345 -0.210108268727
0.52 -0.016345618547 -0.246822151231 -0.229149228724
0.53 0.013297954673 -0.231399387877 -0.244987342798
0.54 0.043247019017 -0.212833206582 -0.257289187069
0.55 0.073212862071 -0.191260247069 -0.265758534051
0.56 0.102893106034 -0.166860004934 -0.270142840681
0.57 0.131973496458 -0.139855518575 -0.270239673429
0.58 0.160129930055 -0.11051365754 -0.265902987658
0.59 0.187030732834 -0.079144969363 -0.257049170206
0.6 0.2123392 -0.04610304 -0.2436627456
0.61 0.235716409292 -0.011783321028 -0.225801637435
0.62 0.256824319601 0.02337862523 -0.203601867119
0.63 0.275329166935 0.058909513534 -0.177281562541
0.64 0.290905170004 0.094301409436 -0.147144139129
0.65 0.303238557872 0.129015543927 -0.113580505335
0.66 0.312031932362 0.162486926193 -0.07707013368
0.67 0.317008978076 0.194129813824 -0.038180827271
0.68 0.317919533105 0.22334410204 0.002433000041
0.69 0.314545033718 0.249522695728 0.044033723754
0.7 0.306704346484 0.272059930352 0.085805795532
0.71 0.294260001544 0.290361110115 0.126863136156
0.72 0.27712484088 0.303853234108 0.166258867468
0.73 0.255269095706 0.311996983522 0.20299763001
0.74 0.228727907242 0.314300045452 0.236050747388
0.75 0.197609305382 0.310331851244 0.264374513179
0.76 0.16210265994 0.299739809819 0.286931891432
0.77 0.12248761939 0.28226711894 0.302717937559
0.78 0.079143552173 0.257772239914 0.310789262597
0.79 0.032559505911 0.226250123825 0.310297880541
0.8 -0.0166553 0.18785528 0.3005297956
0.81 -0.067760432684 0.142926780077 0.280948703955
0.82 -0.119872639067 0.092015293715 0.251245202768
0.83 -0.171953658023 0.035912254722 0.211391917917
0.84 -0.222797435077 -0.024318740874 0.161704981134
0.85 -0.271016723134 -0.087308200485 0.102912307038
0.86 -0.315029052522 -0.151344557222 0.036229140768
0.87 -0.353042053409 -0.21433543874 -0.036558632169
0.88 -0.383038113483 -0.273766269762 -0.113002900907
0.89 -0.402758353549 -0.326656092473 -0.189892934177
0.9 -0.409685903516 -0.369510485977 -0.263145617856
0.91 -0.401028461039 -0.39827146303 -0.327685744643
0.92 -0.373700114874 -0.408264219229 -0.377315751825
0.93 -0.324302414804 -0.394140606769 -0.404574278837
0.94 -0.249104669788 -0.34981920177 -0.400582891552
0.95 -0.1440234558 -0.268421831059 -0.354880294841
0.96 -0.004601314589 -0.142206421099 -0.255243328955
0.97 0.174015375581 0.037503971426 -0.087494018685
0.98 0.39709937637 0.280396091123 0.164708082938
0.99 0.670366432335 0.597245524499 0.520089042482
1 1 1 1

x P11(x) P12(x)
0 0 0.2255859375
0.01 -0.027011695339 0.223828565654
0.02 -0.053672531282 0.218582783894
0.03 -0.079635857057 0.209927235634
0.04 -0.104563396211 0.197991804203
0.05 -0.128129326742 0.182955843569
0.06 -0.150024233735 0.165045729715
0.07 -0.169958893497 0.144531760756
0.08 -0.187667849509 0.121724441506
0.09 -0.202912742106 0.0969701955
0.1 -0.215485355716 0.070646554426
0.11 -0.225210349679 0.043156881436
0.12 -0.231947641207 0.014924690816
0.13 -0.235594411757 -0.013612368023
0.14 -0.236086711201 -0.042008789441
0.15 -0.233400637412 -0.069817676305
0.16 -0.227553072435 -0.096597310094
0.17 -0.218601960161 -0.1219177431
0.18 -0.206646114367 -0.145367327559
0.19 -0.191824550094 -0.166559095406
0.2 -0.17431533568 -0.185136902144
0.21 -0.154333967123 -0.200781248933
0.22 -0.13213127107 -0.213214698615
0.23 -0.107990847312 -0.22220680389
0.24 -0.082226066397 -0.227578469305
0.25 -0.055176642723 -0.229205673153
0.26 -0.027204808189 -0.227022480724
0.27 0.001308883745 -0.22102328666
0.28 0.029970089087 -0.211264231409
0.29 0.058375500325 -0.197863744918
0.3 0.086117925852 -0.181002179691
0.31 0.112791573918 -0.160920505258
0.32 0.13799748908 -0.137918046665
0.33 0.161349085266 -0.112349261063
0.34 0.182477715914 -0.084619558454
0.35 0.201038218358 -0.055180185365
0.36 0.216714366684 -0.02452220334
0.37 0.229224164713 0.006830392245
0.38 0.238324908658 0.038328353634
0.39 0.243817947422 0.069405588911
0.4 0.24555306736 0.099488209276
0.41 0.243432427912 0.128004113565
0.42 0.237413974613 0.154392994245
0.43 0.227514256858 0.178116635591
0.44 0.213810579372 0.198669361712
0.45 0.196442418747 0.215588479792
0.46 0.175612039632 0.228464552557
0.47 0.151584249336 0.236951323693
0.48 0.12468523475 0.240775111074
0.49 0.095300431641 0.239743475346
0.5 0.063871383667 0.233752965927
0.51 0.030891556853 0.222795743157
0.52 -0.003098915033 0.206964874348
0.53 -0.03751956787 0.186458103204
0.54 -0.071757028685 0.16157989679
0.55 -0.105173508873 0.132741582277
0.56 -0.137116341551 0.100459397359
0.57 -0.166928518654 0.065350294014
0.58 -0.193960164934 0.028125355335
0.59 -0.217580865929 -0.010419289866
0.6 -0.23719274496 -0.049414139904
0.61 -0.252244160478 -0.087930629977
0.62 -0.26224386929 -0.124998086481
0.63 -0.266775473432 -0.159623285174
0.64 -0.265511938569 -0.190812517109
0.65 -0.258229939736 -0.217596003364
0.66 -0.244823755885 -0.239054428655
0.67 -0.225318397994 -0.254347284426
0.68 -0.199881616347 -0.262742623343
0.69 -0.168834390917 -0.263647728762
0.7 -0.132659464473 -0.256640094072
0.71 -0.092007431006 -0.24149798717
0.72 -0.04769984227 -0.218229744178
0.73 -0.00072874247 -0.187100793015
0.74 0.047748014535 -0.148657251157
0.75 0.096416370012 -0.103744771855
0.76 0.143821353552 -0.053521128806
0.77 0.188388896447 0.000539170245
0.78 0.228455065655 0.056650165773
0.79 0.262303690903 0.112731781479
0.8 0.28821343328 0.166441618396
0.81 0.304515423045 0.215223882319
0.82 0.309662677684 0.256378405889
0.83 0.30231259837 0.287153033817
0.84 0.281423934177 0.304862967985
0.85 0.246369698679 0.307041019313
0.86 0.197067623136 0.291623086431
0.87 0.134129834333 0.257173578239
0.88 0.059033553533 0.203155919456
0.89 -0.025685274095 0.130253726269
0.9 -0.116213392519 0.040748714272
0.91 -0.207214540894 -0.06103809582
0.92 -0.291554375725 -0.168234776688
0.93 -0.359993599818 -0.270828836075
0.94 -0.400846751049 -0.354991245884
0.95 -0.399603961044 -0.402305275465
0.96 -0.338512845521 -0.388890584218
0.97 -0.196117534079 -0.284412331648
0.98 0.053248312331 -0.050964329366
0.99 0.440017813474 0.358185512124
1 1 1

x P2'(x) P3'(x) P4'(x)
0.01 0.03 -1.49925 -0.0749825
0.02 0.06 -1.497 -0.14986
0.03 0.09 -1.49325 -0.2245275
0.04 0.12 -1.488 -0.29888
0.05 0.15 -1.48125 -0.3728125
0.06 0.18 -1.473 -0.44622
0.07 0.21 -1.46325 -0.5189975
0.08 0.24 -1.452 -0.59104
0.09 0.27 -1.43925 -0.6622425
0.1 0.3 -1.425 -0.7325
0.11 0.33 -1.40925 -0.8017075
0.12 0.36 -1.392 -0.86976
0.13 0.39 -1.37325 -0.9365525
0.14 0.42 -1.353 -1.00198
0.15 0.45 -1.33125 -1.0659375
0.16 0.48 -1.308 -1.12832
0.17 0.51 -1.28325 -1.1890225
0.18 0.54 -1.257 -1.24794
0.19 0.57 -1.22925 -1.3049675
0.2 0.6 -1.2 -1.36
0.21 0.63 -1.16925 -1.4129325
0.22 0.66 -1.137 -1.46366
0.23 0.69 -1.10325 -1.5120775
0.24 0.72 -1.068 -1.55808
0.25 0.75 -1.03125 -1.6015625
0.26 0.78 -0.993 -1.64242
0.27 0.81 -0.95325 -1.6805475
0.28 0.84 -0.912 -1.71584
0.29 0.87 -0.86925 -1.7481925
0.3 0.9 -0.825 -1.7775
0.31 0.93 -0.77925 -1.8036575
0.32 0.96 -0.732 -1.82656
0.33 0.99 -0.68325 -1.8461025
0.34 1.02 -0.633 -1.86218
0.35 1.05 -0.58125 -1.8746875
0.36 1.08 -0.528 -1.88352
0.37 1.11 -0.47325 -1.8885725
0.38 1.14 -0.417 -1.88974
0.39 1.17 -0.35925 -1.8869175
0.4 1.2 -0.3 -1.88
0.41 1.23 -0.23925 -1.8688825
0.42 1.26 -0.177 -1.85346
0.43 1.29 -0.11325 -1.8336275
0.44 1.32 -0.048 -1.80928
0.45 1.35 0.01875 -1.7803125
0.46 1.38 0.087 -1.74662
0.47 1.41 0.15675 -1.7080975
0.48 1.44 0.228 -1.66464
0.49 1.47 0.30075 -1.6161425
0.5 1.5 0.375 -1.5625
0.51 1.53 0.45075 -1.5036075
0.52 1.56 0.528 -1.43936
0.53 1.59 0.60675 -1.3696525
0.54 1.62 0.687 -1.29438
0.55 1.65 0.76875 -1.2134375
0.56 1.68 0.852 -1.12672
0.57 1.71 0.93675 -1.0341225
0.58 1.74 1.023 -0.93554
0.59 1.77 1.11075 -0.8308675
0.6 1.8 1.2 -0.72
0.61 1.83 1.29075 -0.6028325
0.62 1.86 1.383 -0.47926
0.63 1.89 1.47675 -0.3491775
0.64 1.92 1.572 -0.21248
0.65 1.95 1.66875 -0.0690625
0.66 1.98 1.767 0.08118
0.67 2.01 1.86675 0.2383525
0.68 2.04 1.968 0.40256
0.69 2.07 2.07075 0.5739075
0.7 2.1 2.175 0.7525
0.71 2.13 2.28075 0.9384425
0.72 2.16 2.388 1.13184
0.73 2.19 2.49675 1.3327975
0.74 2.22 2.607 1.54142
0.75 2.25 2.71875 1.7578125
0.76 2.28 2.832 1.98208
0.77 2.31 2.94675 2.2143275
0.78 2.34 3.063 2.45466
0.79 2.37 3.18075 2.7031825
0.8 2.4 3.3 2.96
0.81 2.43 3.42075 3.2252175
0.82 2.46 3.543 3.49894
0.83 2.49 3.66675 3.7812725
0.84 2.52 3.792 4.07232
0.85 2.55 3.91875 4.3721875
0.86 2.58 4.047 4.68098
0.87 2.61 4.17675 4.9988025
0.88 2.64 4.308 5.32576
0.89 2.67 4.44075 5.6619575
0.9 2.7 4.575 6.0075
0.91 2.73 4.71075 6.3624925
0.92 2.76 4.848 6.72704
0.93 2.79 4.98675 7.1012475
0.94 2.82 5.127 7.48522
0.95 2.85 5.26875 7.8790625
0.96 2.88 5.412 8.28288
0.97 2.91 5.55675 8.6967775
0.98 2.94 5.703 9.12086
0.99 2.97 5.85075 9.5552325
0.9999999999 3 6 9.999977795541

x P5'(x) P6'(x) P7'(x)
0.01 1.87237539375 0.131171258662 -2.181595915437
0.02 1.8645063 0.2618702772 -2.163909637988
0.03 1.85140689375 0.391625854987 -2.134519028801
0.04 1.8331008 0.5199688704 -2.093553631232
0.05 1.80962109375 0.646433320312 -2.041194333008
0.06 1.7810103 0.7705573596 -1.977672893252
0.07 1.74732039375 0.891884340638 -1.903271334378
0.08 1.7086128 1.0099638528 -1.818321198848
0.09 1.66495839375 1.124352761962 -1.723202670792
0.1 1.6164375 1.23461625 -1.6183435625
0.11 1.56313989375 1.340328854288 -1.50421816577
0.12 1.5051648 1.4410755072 -1.381345968128
0.13 1.44262089375 1.536452575612 -1.250290233911
0.14 1.3756263 1.6260689004 -1.111656450212
0.15 1.30430859375 1.709546835938 -0.966090637695
0.16 1.2288048 1.7865232896 -0.814277526272
0.17 1.14926139375 1.856650761262 -0.656938595643
0.18 1.0658343 1.9195983828 -0.494829980708
0.19 0.97868889375 1.975052957588 -0.328740241835
0.2 0.888 2.02272 -0.159488
0.21 0.79395189375 2.062324774912 0.01208056321
0.22 0.6967383 2.0936133372 0.185094340732
0.23 0.59656239375 2.116353571238 0.358660070292
0.24 0.4936368 2.1303362304 0.531865239808
0.25 0.38818359375 2.135375976562 0.70378112793
0.26 0.2804343 2.1313124196 0.873465979708
0.27 0.17062989375 2.118011156888 1.039968317404
0.28 0.0590208 2.0953648128 1.202330386432
0.29 -0.05413310625 2.063294078212 1.359591736435
0.3 -0.1685625 2.02174875 1.5107929375
0.31 -0.28398860625 1.970708770538 1.654979431503
0.32 -0.4001232 1.9101852672 1.791205518592
0.33 -0.51666860625 1.840221591863 1.918538478807
0.34 -0.6333177 1.7608943604 2.036062828828
0.35 -0.74975390625 1.672314492188 2.142884713867
0.36 -0.8656512 1.5746282496 2.238136434688
0.37 -0.98067410625 1.468018277512 2.320981109764
0.38 -1.0944777 1.3527046428 2.390617472572
0.39 -1.20670760625 1.228945873838 2.446284804018
0.4 -1.317 1.09704 2.487268
0.41 -1.42498160625 0.957325591163 2.512902774108
0.42 -1.5302697 0.8101827972 2.522580995452
0.43 -1.63247210625 0.656034387488 2.515756161634
0.44 -1.7311872 0.4953467904 2.491949006848
0.45 -1.82600390625 0.328631132812 2.450753245117
0.46 -1.9165017 0.1564442796 2.391841448668
0.47 -2.00225060625 -0.020610126863 2.314971061437
0.48 -2.0828112 -0.2018806272 2.219990547712
0.49 -2.15773460625 -0.386666905537 2.106845675913
0.5 -2.2265625 -0.57421875 1.9755859375
0.51 -2.28882710625 -0.763735013212 1.826371101025
0.52 -2.3440512 -0.9543625728 1.659477901312
0.53 -2.39174810625 -1.145195291888 1.475306863774
0.54 -2.4314217 -1.3352729796 1.274389263868
0.55 -2.46256640625 -1.523580351563 1.05739422168
0.56 -2.4846672 -1.7090459904 0.825135931648
0.57 -2.49719960625 -1.890541306237 0.578581027422
0.58 -2.4996297 -2.0668794972 0.318856081852
0.59 -2.49141410625 -2.236814509912 0.04725524212
0.6 -2.472 -2.39904 -0.234752
0.61 -2.44082510625 -2.552188292588 -0.525512902745
0.62 -2.3973177 -2.6948293428 -0.823183433828
0.63 -2.34089660625 -2.825469696262 -1.125720094773
0.64 -2.2709712 -2.9425514496 -1.430871610112
0.65 -2.18694140625 -3.044451210938 -1.736170481445
0.66 -2.0881977 -3.1294790604 -2.038924406372
0.67 -1.97412110625 -3.195877510613 -2.336207562281
0.68 -1.8440832 -3.2418204672 -2.624851755008
0.69 -1.69744610625 -3.265412189287 -2.90143743236
0.7 -1.5335625 -3.26468625 -3.1622845625
0.71 -1.35177560625 -3.237604496963 -3.403443377202
0.72 -1.1514192 -3.1820560128 -3.620684979968
0.73 -0.93181760625 -3.095856075637 -3.809491819008
0.74 -0.6922857 -2.9767451196 -3.965048025092
0.75 -0.43212890625 -2.822387695312 -4.082229614258
0.76 -0.1506432 -2.6303714304 -4.155594555392
0.77 0.15288489375 -2.398205989988 -4.179372702671
0.78 0.4791783 -2.1233220372 -4.147455592868
0.79 0.82896939375 -1.803070193663 -4.053386107527
0.8 1.203 -1.43472 -3.890348
0.81 1.60202139375 -1.015458876337 -3.651155287347
0.82 2.0267943 -0.5423910828 -3.328241507108
0.83 2.47808889375 -0.012536680013 -2.913648838931
0.84 2.9566848 0.5771695104 -2.399017091072
0.85 3.46337109375 1.229878945313 -1.775572551758
0.86 3.9989463 1.9488303996 -1.034116705412
0.87 4.56421839375 2.737351005638 -0.165014813748
0.88 5.1600048 3.5988572928 0.841815638272
0.89 5.78713239375 4.536856226962 1.996916631618
0.9 6.4464375 5.55494625 3.3113014375
0.91 7.13876589375 6.656818319288 4.79646657682
0.92 7.8649728 7.8462569472 6.464403914753
0.93 8.62592289375 9.127141240613 8.327612890459
0.94 9.4224903 10.5034459404 10.399112881949
0.95 10.25555859375 11.979242460937 12.692455706056
0.96 11.1260208 13.5586999296 15.221738253568
0.97 12.03477939375 15.246086226263 18.001615259486
0.98 12.9827463 17.0457690228 21.047312208412
0.99 13.970842893749 18.962216822586 24.374638375077
0.9999999999 14.99997335465 21.000186517453 27.999857891465

x P8'(x) P9'(x) P10'(x)
0.01 -0.196658493802 2.450116411874 0.270234117364
0.02 -0.392019301285 2.417737522432 0.537659252375
0.03 -0.584791486123 2.364053450161 0.799491703091
0.04 -0.773697591706 2.289483539841 1.052998156371
0.05 -0.957480330322 2.194611339537 1.295520452865
0.06 -1.134909211532 2.080181080438 1.524499838558
0.07 -1.304787089457 1.947093171619 1.737500534758
0.08 -1.465956608717 1.796398725222 1.932232461056
0.09 -1.617306528753 1.629293131017 2.106572949063
0.1 -1.75777790625 1.447108702734 2.258587288633
0.11 -1.886370115403 1.251306422016 2.386547952893
0.12 -2.002146685747 1.043466809278 2.488952353625
0.13 -2.104240937289 0.825279954223 2.564538984425
0.14 -2.191861392664 0.598534742171 2.612301815646
0.15 -2.264296946045 0.365107315855 2.631502812293
0.16 -2.32092176855 0.126948815749 2.621682453931
0.17 -2.361199929856 -0.113927554562 2.582668144147
0.18 -2.384689715759 -0.355460087981 2.514580406299
0.19 -2.391047621418 -0.595552705084 2.417836772093
0.2 -2.380032 -0.8320896 2.29315328
0.21 -2.351506346455 -1.062950340717 2.141543511677
0.22 -2.305442196169 -1.286025360033 1.964315106306
0.23 -2.241921618199 -1.499231769973 1.763063705245
0.24 -2.161139282842 -1.700529429033 1.539664292447
0.25 -2.063404083252 -1.887937188148 1.296259909868
0.26 -1.949140290848 -2.059549237865 1.035247741492
0.27 -1.81888822423 -2.213551475732 0.759262574644
0.28 -1.673304411341 -2.348237809484 0.471157662995
0.29 -1.513161224601 -2.46202630815 0.173983032012
0.3 -1.33934596875 -2.553475109766 -0.129038715352
0.31 -1.152859401116 -2.621297990926 -0.434539017266
0.32 -0.954813664051 -2.664379499971 -0.739032302146
0.33 -0.746429609258 -2.68178955215 -1.038947155489
0.34 -0.52903349374 -2.672797381658 -1.330659572013
0.35 -0.3040530271 -2.636884742006 -1.610528140371
0.36 -0.073012749926 -2.573758242718 -1.874930986769
0.37 0.162471277013 -2.483360706933 -2.120304282208
0.38 0.400697493037 -2.365881431016 -2.343182095812
0.39 0.639885587543 -2.221765223843 -2.54023735379
0.4 0.878184 -2.0517201 -2.70832364
0.41 1.113678190209 -1.856723497652 -2.844517549866
0.42 1.344399699107 -1.638026888431 -2.946161284527
0.43 1.568336020377 -1.397158643219 -3.010905146541
0.44 1.783441303142 -1.135925014266 -3.036749572299
0.45 1.987647906006 -0.856409090639 -3.022086309447
0.46 2.178878822716 -0.560967580547 -2.965738320126
0.47 2.355060999718 -0.252225270648 -2.866997962674
0.48 2.514139565875 0.066932991017 -2.725662975631
0.49 2.654092994608 0.393372945234 -2.542069758439
0.5 2.77294921875 0.723724365234 -2.317123413086
0.51 2.868802718363 1.054397457373 -2.052323980188
0.52 2.939832601805 1.381602386018 -1.749788271576
0.53 2.984321700301 1.701372093218 -1.412266669367
0.54 3.000676696304 2.009588587158 -1.043154228756
0.55 2.987449305908 2.302012876891 -0.646495388397
0.56 2.943358535578 2.574318734233 -0.22698155817
0.57 2.867314033479 2.822130467202 0.210059180557
0.58 2.758440555673 3.041064892784 0.658681062416
0.59 2.616103567438 3.22677770029 1.112349149541
0.6 2.439936 3.3750144 1.56397824
0.61 2.229866182941 3.481666055225 2.005983083405
0.62 1.986146972543 3.542829999382 2.430340851921
0.63 1.709386096356 3.554875743117 2.828666853505
0.64 1.400577734246 3.514516279951 3.192304513527
0.65 1.061135356201 3.418885002379 3.512430690819
0.66 0.69292583716 3.265618443785 3.780177434829
0.67 0.29830486914 3.052945065003 3.986771331789
0.68 -0.119846309069 2.77978030778 4.123691629689
0.69 -0.558082844375 2.44582814084 4.182848374463
0.7 -1.01235684375 2.051689327734 4.15678183293
0.71 -1.477976570215 1.598976649041 4.038884521968
0.72 -1.949564240179 1.09043731499 3.823647207873
0.73 -2.421012401863 0.530082807994 3.506930285057
0.74 -2.885438874532 -0.076673601973 3.086261989065
0.75 -3.335140228271 -0.722871422768 2.561164945364
0.76 -3.761543784038 -1.399849336406 1.93351260252
0.77 -4.155158113707 -2.097083173048 1.207917146153
0.78 -4.505522019851 -2.802015205926 0.39215053852
0.79 -4.801151974985 -3.499874507038 -0.502399622311
0.8 -5.029488 -4.1734881 -1.460237679999
0.81 -5.17683796151 -4.803082642983 -2.461229140046
0.82 -5.228320267861 -5.366076371251 -3.480029687276
0.83 -5.167804943513 -5.836861025323 -4.485472103802
0.84 -4.97785306153 -6.186573487374 -5.439909138134
0.85 -4.639654513916 -6.382856845033 -6.298510323124
0.86 -4.132964099516 -6.389610598278 -7.008510686744
0.87 -3.436035909217 -6.166729721696 -7.508409245276
0.88 -2.525555988172 -5.669832290941 -7.727115113641
0.89 -1.3765732548 -4.849975378711 -7.583039011778
0.9 0.03757134375 -3.653358922266 -6.983127889805
0.91 1.745317459899 -2.021017260841 -5.821840337663
0.92 3.776959777997 0.111501961884 -3.980060387357
0.93 6.164724271 2.814471838802 -1.323947257599
0.94 8.942846301752 6.164333495556 2.296281468129
0.95 12.147650589111 10.244056957451 7.047635798995
0.96 15.817633059224 15.143515905558 13.115711058341
0.97 19.993544602202 20.959876644375 20.70612005933
0.98 24.718476754467 27.798001606704 30.046002485829
0.99 30.037949327025 35.770867724777 41.385614292515
0.9999999999 35.999120703437 45.000888178346 55.001856292744

x P11'(x) P12'(x)
0.01 -2.689453136596 -0.351034875435
0.02 -2.636929586075 -0.6968089671
0.03 -2.550090817882 -1.032133009221
0.04 -2.42998004869 -1.351959956477
0.05 -2.27804282594 -1.651454062201
0.06 -2.096112208824 -1.926057537352
0.07 -1.886389910171 -2.171554015679
0.08 -1.651423544287 -2.384128077651
0.09 -1.394080156746 -2.560420119384
0.1 -1.117516242395 -2.697575892827
0.11 -0.825144487099 -2.793290089735
0.12 -0.520597497093 -2.845843394134
0.13 -0.207688806898 -2.854132485975
0.14 0.109628517412 -2.817692541971
0.15 0.427305338431 -2.736711848175
0.16 0.741241607197 -2.612038212063
0.17 1.047332837478 -2.445176939566
0.18 1.34151749036 -2.238280224136
0.19 1.619824847657 -1.994127880077
0.2 1.8784229376 -1.71609944064
0.21 2.113666063438 -1.408137732156
0.22 2.322141475149 -1.074704128311
0.23 2.500714716604 -0.720725782919
0.24 2.64657317533 -0.351535234686
0.25 2.757267359644 0.02719712723
0.26 2.830749428507 0.409537153142
0.27 2.865408503128 0.78936690079
0.28 2.860102296273 1.160469712005
0.29 2.81418460546 1.51661953948
0.3 2.727528230071 1.851673579246
0.31 2.600542889778 2.159667182846
0.32 2.434187742926 2.434909946698
0.33 2.229978128611 2.672081805638
0.34 1.989986185407 2.866327894003
0.35 1.716835033033 3.013350881852
0.36 1.413686240992 3.109499446968
0.37 1.084220350351 3.15185150618
0.38 0.73261026166 3.138290803332
0.39 0.363487353473 3.067575436922
0.4 -0.0180997476 2.93939690928
0.41 -0.406733763018 2.754428292103
0.42 -0.796684675679 2.51436013157
0.43 -1.181972839786 2.221922761183
0.44 -1.556439089111 1.880893753252
0.45 -1.913821562724 1.496089321742
0.46 -2.24783887864 1.073338591409
0.47 -2.552279191447 0.61943977205
0.48 -2.821094569554 0.142097423608
0.49 -3.048500021192 -0.350159830687
0.5 -3.229076385498 -0.848081588745
0.51 -3.357876185891 -1.341818172568
0.52 -3.430531417182 -1.821063317325
0.53 -3.443362105545 -2.275216730381
0.54 -3.393484341283 -2.693565888515
0.55 -3.278916338179 -3.065486092472
0.56 -3.098680920065 -3.380657413854
0.57 -2.852902674796 -3.629296748478
0.58 -2.542897848039 -3.802402731076
0.59 -2.171254874037 -3.892010766834
0.6 -1.7419032576 -3.89145489408
0.61 -1.260168330905 -3.795632607587
0.62 -0.732809210119 -3.601268141759
0.63 -0.168037070241 -3.307169035441
0.64 0.424489358234 -2.914470073556
0.65 1.03369439035 -2.426857923099
0.66 1.647145636511 -1.85076895052
0.67 2.251147692323 -1.19555182207
0.68 2.830873308638 -0.473585546288
0.69 3.370536339672 0.299657383368
0.7 3.853611033899 1.105614150056
0.71 4.263102508309 1.922713608825
0.72 4.581873531814 2.726550835671
0.73 4.793033038198 3.490169208243
0.74 4.880392093176 4.184466323371
0.75 4.828993353993 4.778741455637
0.76 4.62572038367 5.241403734209
0.77 4.259993515682 5.540861764445
0.78 3.724559308616 5.646617048574
0.79 3.016380984329 5.530585268453
0.8 2.137637607603 5.168671285442
0.81 1.096840140063 4.542625589993
0.82 -0.089927113116 3.642211899452
0.83 -1.397630749069 2.467717658715
0.84 -2.790768883555 1.032841347938
0.85 -4.221698397244 -0.632007253509
0.86 -5.628798642154 -2.475955354625
0.87 -6.934460997258 -4.423423055616
0.88 -8.042893209967 -6.369343382376
0.89 -8.837726996436 -8.173800315968
0.9 -9.179416897243 -9.656035917747
0.91 -8.902417898338 -10.587774778213
0.92 -7.81212882643 -10.685811029012
0.93 -5.681588016796 -9.60380005344
0.94 -2.247907227011 -6.923193805974
0.95 2.791570765835 -2.143255304989
0.96 9.783405997513 5.329915611355
0.97 19.122502251943 16.195416775432
0.98 31.25687134847 31.270713669468
0.99 46.69273761687 51.506024002385
1.00 66.001278976819 78.001284527933










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--Last edited by saucer on 2007-01-02 16:19:11 --

-



Table: Table: Zero-order Second-kind Legendre Functions Qn(x)(Legendre Orthogonal Polynomial Functions)-





x Q2(x) Q3(x) Q4(x)
0 -0 0.666666666667 0
0.01 -0.019998666627 0.666266686667 0.026658666987
0.02 -0.039989332053 0.665066986701 0.053269343574
0.03 -0.059963990275 0.663068287056 0.079784077777
0.04 -0.079914625669 0.660271788853 0.106154994472
0.05 -0.099833208154 0.656679175011 0.132334333929
0.06 -0.119711688319 0.652292611598 0.158274490457
0.07 -0.139541992498 0.647114749578 0.183928051197
0.08 -0.159316017798 0.641148726958 0.209247835123
0.09 -0.179025627046 0.634398171338 0.23418693227
0.1 -0.19866264365 0.626867202876 0.258698743241
0.11 -0.218218846373 0.618560437674 0.282737019032
0.12 -0.237685963991 0.609482991596 0.306255901228
0.13 -0.257055669816 0.599640484537 0.329209962594
0.14 -0.276319576099 0.589039045144 0.351554248134
0.15 -0.295469228255 0.577685316009 0.373244316644
0.16 -0.314496098934 0.565586459363 0.394236282823
0.17 -0.333391581888 0.552750163268 0.414486859988
0.18 -0.352146985634 0.539184648344 0.433953403454
0.19 -0.370753526897 0.524898675048 0.452593954626
0.2 -0.389202323784 0.509901551532 0.470367285874
0.21 -0.407484388707 0.4942031421 0.487232946252
0.22 -0.425590620996 0.477813876312 0.503151308127
0.23 -0.443511799192 0.46074475874 0.518083614787
0.24 -0.461238572996 0.443007379443 0.531992029113
0.25 -0.478761454827 0.424613925175 0.544839683385
0.26 -0.49607081098 0.405577191384 0.556590730315
0.27 -0.51315685232 0.385910595045 0.567210395399
0.28 -0.530009624506 0.365628188373 0.576665030682
0.29 -0.546618997669 0.344744673486 0.584922170046
0.3 -0.562974655534 0.323275418059 0.591950586132
0.31 -0.5790660839 0.301236472063 0.597720349019
0.32 -0.594882558455 0.278644585633 0.602202886796
0.33 -0.610413131849 0.255517228178 0.60537104816
0.34 -0.625646619959 0.231872608792 0.6071991672
0.35 -0.640571587288 0.207729698085 0.607663130543
0.36 -0.655176331403 0.18310825154 0.606740447022
0.37 -0.669448866332 0.158028834498 0.604410320087
0.38 -0.683376904826 0.132512848929 0.600653723157
0.39 -0.696947839373 0.10658256211 0.59545347817
0.4 -0.71014872185 0.080261137381 0.588794337555
0.41 -0.722966241679 0.053572667168 0.580663069952
0.42 -0.735386702338 0.026542208442 0.571048549959
0.43 -0.747395996072 -0.000804179133 0.559941852257
0.44 -0.758979576607 -0.028439392141 0.547336350506
0.45 -0.770122429674 -0.056335239167 0.533227821411
0.46 -0.780809041111 -0.08446239304 0.517614554436
0.47 -0.79102336227 -0.11279033925 0.500497467669
0.48 -0.80074877246 -0.141287320131 0.481880230435
0.49 -0.809968038075 -0.169920274387 0.461769393269
0.5 -0.818663268042 -0.198654771479 0.440174525987
0.51 -0.826815865163 -0.227454940302 0.417108364653
0.52 -0.834406472869 -0.256283391543 0.392586968348
0.53 -0.841414916822 -0.285101133003 0.366629886756
0.54 -0.847820140745 -0.313867477071 0.339260339727
0.55 -0.853600135753 -0.342539939417 0.310505410125
0.56 -0.858731862325 -0.371074127859 0.280396251442
0.57 -0.863191163987 -0.399423620155 0.248968311885
0.58 -0.866952671546 -0.427539829345 0.216261576874
0.59 -0.869989696599 -0.455371854974 0.182320832189
0.6 -0.872274112778 -0.482866318335 0.147195950332
0.61 -0.873776222949 -0.509967179499 0.110942203097
0.62 -0.874464610278 -0.536615533559 0.073620603797
0.63 -0.874305970662 -0.562749383042 0.035298283192
0.64 -0.873264923608 -0.588303382914 -0.003951096157
0.65 -0.871303798045 -0.613208553905 -0.044046881533
0.66 -0.868382388871 -0.637391959114 -0.084900921124
0.67 -0.864457679199 -0.660776337818 -0.126416996692
0.68 -0.859483522185 -0.683279689173 -0.168490188477
0.69 -0.85341027502 -0.704814797007 -0.211006161121
0.7 -0.846184375992 -0.725288684914 -0.253840357026
0.71 -0.837747853426 -0.744601988497 -0.296857080637
0.72 -0.828037752631 -0.762648228483 -0.339908453416
0.73 -0.816985463513 -0.779312964541 -0.382833214566
0.74 -0.804515927076 -0.794472804488 -0.425455336505
0.75 -0.790546693131 -0.807994237011 -0.467582416229
0.76 -0.774986793829 -0.819732247238 -0.509003793455
0.77 -0.757735387297 -0.82952866297 -0.549488332879
0.78 -0.738680111703 -0.837210163749 -0.588781789741
0.79 -0.717695070998 -0.842585863751 -0.626603653388
0.8 -0.694638347213 -0.84544435024 -0.662643329926
0.81 -0.669348897038 -0.845550018402 -0.696555478306
0.82 -0.641642637509 -0.842638485239 -0.727954248186
0.83 -0.611307448717 -0.836410781156 -0.756406073091
0.84 -0.578096707725 -0.826525894052 -0.781420533462
0.85 -0.541720796002 -0.812591054463 -0.802438596512
0.86 -0.501835756853 -0.794148863465 -0.818817221874
0.87 -0.458027857272 -0.770659911602 -0.82980882246
0.88 -0.409792118446 -0.741478798879 -0.83453326144
0.89 -0.356501711781 -0.70582022268 -0.831938712988
0.9 -0.297363064948 -0.662709624505 -0.820745359885
0.91 -0.231347747723 -0.610908902095 -0.799361615794
0.92 -0.157084886082 -0.548799999966 -0.765754335384
0.93 -0.072682717613 -0.474193357987 -0.717237651914
0.94 0.024585929295 -0.38399296692 -0.650107877554
0.95 0.138882877692 -0.273563298263 -0.55896114163
0.96 0.277071115526 -0.135402043886 -0.435278770374
0.97 0.451813704454 0.044080923244 -0.264032911133
0.98 0.691084865518 0.294366129303 -0.013475737385
0.99 1.082649837853 0.706248306965 0.411587813428
0.9999999999 10.359499010447 10.026165673906 9.776165669746

x Q5(x) Q6(x) Q7(x)
0 -0.533333333333 -0 0.457142857143
0.01 -0.532533493328 -0.031978669867 0.455863390412
0.02 -0.530135892992 -0.063829435722 0.452031386381
0.03 -0.526146289445 -0.0954247774 0.445666010497
0.04 -0.520574271481 -0.126637941968 0.436799128437
0.05 -0.513433249955 -0.157343326187 0.425475191101
0.06 -0.504740444309 -0.187416857588 0.411751073848
0.07 -0.494516865212 -0.216736373699 0.395695870172
0.08 -0.482787293309 -0.245181998954 0.377390640134
0.09 -0.469580254043 -0.272636518809 0.356928113893
0.1 -0.454927988518 -0.298985750595 0.334412350762
0.11 -0.43886642037 -0.324118910635 0.309958354288
0.12 -0.421435118611 -0.347928977118 0.283691643909
0.13 -0.402677256383 -0.370313048267 0.255747783818
0.14 -0.382639565585 -0.391172695279 0.226271869729
0.15 -0.361372287313 -0.410414309548 0.195417974323
0.16 -0.338929118038 -0.427949443643 0.163348552207
0.17 -0.315367151458 -0.443695145528 0.130233805305
0.18 -0.290746815956 -0.457574285477 0.096251009674
0.19 -0.265131807557 -0.469515875154 0.061583804816
0.2 -0.238589018311 -0.479455378275 0.026421446621
0.21 -0.211188459997 -0.487335012309 -0.009041974803
0.22 -0.183003183031 -0.493104040595 -0.044608351131
0.23 -0.15410919047 -0.496719054304 -0.080076404221
0.24 -0.124585346977 -0.498144243598 -0.115242565451
0.25 -0.094513282617 -0.497351657353 -0.149901884385
0.26 -0.06397729132 -0.494321450791 -0.183848965108
0.27 -0.033064223872 -0.489042120316 -0.216878928439
0.28 -0.001863375235 -0.481510724855 -0.248788398152
0.29 0.029533633976 -0.471733092975 -0.279376509195
0.3 0.061032982064 -0.459724014975 -0.308445935826
0.31 0.092538777103 -0.445507419196 -0.335803937425
0.32 0.123953194288 -0.429116531681 -0.361263419646
0.33 0.155176620064 -0.410594018328 -0.38464400843
0.34 0.186107803293 -0.389992108614 -0.405773134262
0.35 0.216644013774 -0.367372699948 -0.424487123915
0.36 0.246681208439 -0.342807441616 -0.440632296771
0.37 0.276114205579 -0.316377797288 -0.454066062633
0.38 0.304836867496 -0.288175084942 -0.464658017799
0.39 0.332742291987 -0.258300493037 -0.472291035946
0.4 0.359723013134 -0.226865071664 -0.476862350208
0.41 0.38567121189 -0.193989697356 -0.478284622607
0.42 0.410478937015 -0.159805010131 -0.476486996772
0.43 0.434038336953 -0.12445132125 -0.471416129643
0.44 0.456241903314 -0.088078490082 -0.463037197593
0.45 0.476982726677 -0.050845768334 -0.451334872117
0.46 0.496154765505 -0.012921609787 -0.436314259937
0.47 0.513653129048 0.025516556472 -0.418001802035
0.48 0.529374375201 0.06428259148 -0.396446125767
0.49 0.543216824373 0.103181952838 -0.371718843809
0.5 0.555080890572 0.142012044702 -0.343915293267
0.51 0.564869430993 0.180562614101 -0.313155207781
0.52 0.572488115608 0.218616196589 -0.279583314958
0.53 0.577845818367 0.25594861455 -0.24336985085
0.54 0.580855031871 0.29232953178 -0.20471098259
0.55 0.581432307558 0.32752306835 -0.163829129521
0.56 0.579498723741 0.361288480172 -0.120973172399
0.57 0.574980384119 0.393380908166 -0.076418539314
0.58 0.567808949733 0.423552202487 -0.030467155949
0.59 0.557922207764 0.451551827907 0.016552753352
0.6 0.545264681026 0.477127857186 0.064287028556
0.61 0.5297882826 0.500028060126 0.112356117315
0.62 0.511453020685 0.520001097014 0.160355816832
0.63 0.490227759574 0.536797826314 0.207858234296
0.64 0.466091043558 0.550172737906 0.25441298829
0.65 0.43903199173 0.559885524756 0.299548676258
0.66 0.409051272996 0.565702807929 0.342774636293
0.67 0.376162172244 0.567400032149 0.383583035223
0.68 0.340391760642 0.564763551998 0.421451319402
0.69 0.301782185493 0.55759293225 0.455845069903
0.7 0.260392098078 0.545703490056 0.486221310148
0.71 0.216298241743 0.528929111866 0.512032321724
0.72 0.16959722716 0.507125384364 0.532730033527
0.73 0.120407527693 0.4801730867 0.547771060947
0.74 0.068871735366 0.447982101401 0.556622486183
0.75 0.0151591277 0.410495814112 0.55876848877
0.76 -0.040531391656 0.367696088838 0.553717958237
0.77 -0.097967898995 0.319608926652 0.541013249965
0.78 -0.156881501797 0.266310943881 0.520240283105
0.79 -0.216961704116 0.207936843028 0.491040228942
0.8 -0.277850914902 0.144688099749 0.453123103829
0.81 -0.339137872648 0.076843157705 0.406283669504
0.82 -0.400349682131 0.004769518018 0.350420164979
0.83 -0.460942048273 -0.07106175588 0.285556563385
0.84 -0.520287131354 -0.150058404399 0.21186928744
0.85 -0.577658209093 -0.231485212077 0.129719665873
0.86 -0.63220996869 -0.314436699072 0.03969393093
0.87 -0.682952686691 -0.397802183222 -0.057346653156
0.88 -0.728717647017 -0.480220085988 -0.160201700228
0.89 -0.768109640063 -0.560016635212 -0.267247804147
0.9 -0.799439783409 -0.635121176054 -0.376325579912
0.91 -0.820627204995 -0.702945040505 -0.484582371314
0.92 -0.829049179422 -0.76020100314 -0.588244131573
0.93 -0.821301142914 -0.802620405407 -0.682267691984
0.94 -0.792788155286 -0.824481689647 -0.759776759396
0.95 -0.736972913578 -0.817760206456 -0.811071581181
0.96 -0.643840080097 -0.770426232326 -0.821696985549
0.97 -0.496266201434 -0.662499302272 -0.768074141864
0.98 -0.259264104189 -0.454581392705 -0.605111759705
0.99 0.168450837956 -0.037251573633 -0.212876111485
0.9999999999 9.576165664657 9.409498991995 9.266641842251

x Q8(x) Q9(x) Q10(x)
0 0 -0.406349206349 -0
0.01 0.036528774703 -0.404521914622 -0.040561813611
0.02 0.072801933246 -0.399055381527 -0.080685844419
0.03 0.108565393315 -0.389995525932 -0.119938598962
0.04 0.143568133855 -0.377418521831 -0.157895128129
0.05 0.177563709579 -0.361430263963 -0.194143213698
0.06 0.210311746197 -0.342165623296 -0.228287452633
0.07 0.241579409947 -0.319787495949 -0.259953205914
0.08 0.271142845105 -0.294485650192 -0.288790379424
0.09 0.298788573177 -0.266475377132 -0.314477005349
0.1 0.324314847539 -0.235995951698 -0.336722593607
0.11 0.347532957377 -0.203308911556 -0.355271224155
0.12 0.368268474858 -0.168696162507 -0.369904352424
0.13 0.386362439539 -0.132457919907 -0.380443301802
0.14 0.401672474173 -0.094910496589 -0.386751418848
0.15 0.414073826133 -0.056383948661 -0.388735868888
0.16 0.42346032885 -0.017219591465 -0.38634905177
0.17 0.429745277778 0.022232601149 -0.379589619829
0.18 0.432862215558 0.061616700246 -0.368503082518
0.19 0.432765621225 0.100573613115 -0.353181984768
0.2 0.429431498474 0.138743946871 -0.333765648815
0.21 0.422857858191 0.175770928019 -0.310439472093
0.22 0.413065090679 0.21130336091 -0.283433776751
0.23 0.400096223196 0.244998607385 -0.253022209449
0.24 0.384017058695 0.276525569232 -0.219519693256
0.25 0.364916191878 0.305567654507 -0.1832799368
0.26 0.342904898952 0.331825708248 -0.144692509183
0.27 0.318116897754 0.355020887578 -0.104179492651
0.28 0.290707975219 0.374897460806 -0.062191728548
0.29 0.260855479478 0.39122550971 -0.01920467568
0.3 0.2287576742 0.403803513892 0.024286096138
0.31 0.194632953168 0.412460795844 0.067769750901
0.32 0.158718913434 0.417059805138 0.110725339434
0.33 0.121271285821 0.417498220099 0.152627226764
0.34 0.082562721945 0.413710845216 0.192950756258
0.35 0.042881437385 0.40567128264 0.231178109309
0.36 0.002529711094 0.393393356229 0.266804315676
0.37 -0.038177758325 0.3769322668 0.299343366053
0.38 -0.078915638357 0.356385457623 0.328334374925
0.39 -0.119349888628 0.331893169552 0.353347738403
0.4 -0.15913982495 0.303638665778 0.373991228447
0.41 -0.197940318443 0.271848106812 0.389915961805
0.42 -0.235404126094 0.236790057096 0.400822179047
0.43 -0.271184348431 0.198774605568 0.406464766337
0.44 -0.304937009193 0.158152083554 0.406658450124
0.45 -0.336323751056 0.115311364595 0.401282592679
0.46 -0.365014640632 0.070677732195 0.390285514507
0.47 -0.390691074956 0.024710303042 0.373688268077
0.48 -0.413048780735 -0.022101004963 0.351587786135
0.49 -0.431800896483 -0.069238968581 0.324159327086
0.5 -0.446681126552 -0.116163025506 0.291658139666
0.51 -0.457446954779 -0.162313715076 0.254420269392
0.52 -0.463882904099 -0.207117594731 0.212862430095
0.53 -0.465803827014 -0.249992630511 0.167480865389
0.54 -0.46305821018 -0.290354056526 0.118849127167
0.55 -0.455531474625 -0.327620694619 0.067614701285
0.56 -0.44314925117 -0.361221721327 0.014494414561
0.57 -0.425880608538 -0.390603864691 -0.039731437776
0.58 -0.403741209271 -0.415239008424 -0.09422629894
0.59 -0.376796366023 -0.434632175336 -0.148105939131
0.6 -0.345163967912 -0.448329855683 -0.200448464358
0.61 -0.309017243432 -0.455928639212 -0.250305773758
0.62 -0.26858732282 -0.457084101909 -0.29671648151
0.63 -0.224165558763 -0.451519889858 -0.338720305273
0.64 -0.17610555972 -0.439036932896 -0.375373906654
0.65 -0.124824884972 -0.419522709889 -0.405768150239
0.66 -0.070806344525 -0.392960475102 -0.429046725705
0.67 -0.014598840132 -0.35943834121 -0.444426052241
0.68 0.043182324239 -0.319158098557 -0.451216355151
0.69 0.101855743468 -0.272443632038 -0.448843770723
0.7 0.160674915771 -0.219748775946 -0.436873296202
0.71 0.218830055412 -0.161664422774 -0.415032356193
0.72 0.275450833943 -0.098924673417 -0.383234703783
0.73 0.329610188809 -0.032411782718 -0.341604312558
0.74 0.380329360853 0.036840385563 -0.290498842666
0.75 0.426584349985 0.107644728016 -0.230532177563
0.76 0.467314012754 0.178661486543 -0.162595424911
0.77 0.501430068816 0.248401511232 -0.087875651002
0.78 0.527829338146 0.315232750996 -0.007871467355
0.79 0.545408601471 0.377390631802 0.075595597011
0.8 0.553082568463 0.432993122274 0.16037523424
0.81 0.549805560067 0.480061467343 0.243989594181
0.82 0.53459767539 0.516547808345 0.32364357755
0.83 0.506576438163 0.540371226155 0.396246629301
0.84 0.464995231568 0.549464178585 0.458449120611
0.85 0.409290278052 0.541831910097 0.506697284559
0.86 0.339138575313 0.515628280404 0.537311892398
0.87 0.254530182358 0.469252735814 0.546597608178
0.88 0.155859769863 0.40147508433 0.530992548124
0.89 0.04404478264 0.311597777169 0.487271536817
0.9 -0.079318387053 0.199670368597 0.41282287865
0.91 -0.211741760614 0.06677932598 0.306029039172
0.92 -0.349545249217 -0.084548293908 0.166800306545
0.93 -0.487411433166 -0.249759246942 -0.002654299498
0.94 -0.617685059995 -0.421377020394 -0.196662804429
0.95 -0.729181073329 -0.587522409425 -0.404214983015
0.96 -0.804931620704 -0.729212018388 -0.605644262906
0.97 -0.817247956027 -0.814647295553 -0.76587180528
0.98 -0.71413413984 -0.784064521344 -0.817207412887
0.99 -0.362556155015 -0.488756799669 -0.593051000664
0.9999999999 9.141641834488 9.030530714749 8.930530705269

x Q11(x) Q12(x)
0 0.369408369408 0
0.01 0.366972833215 0.044215308447
0.02 0.359696887328 0.087750404732
0.03 0.347672176543 0.129934865866
0.04 0.331050300971 0.170117723859
0.05 0.310041115023 0.207676886079
0.06 0.284910367513 0.242028190511
0.07 0.255976704254 0.272633979908
0.08 0.223608060408 0.299011083735
0.09 0.188217475564 0.320738102771
0.1 0.150258370036 0.337461898397
0.11 0.11021932616 0.348903196741
0.12 0.06861842336 0.354861227095
0.13 0.025997180468 0.355217324119
0.14 -0.017085836866 0.349937434385
0.15 -0.060061681853 0.339073479614
0.16 -0.102357899936 0.322763541476
0.17 -0.143405541298 0.30123084597
0.18 -0.182646241307 0.274781539057
0.19 -0.219539295488 0.243801259264
0.2 -0.253568653976 0.20875052739
0.21 -0.284249759283 0.170158987974
0.22 -0.311136150699 0.128618551811
0.23 -0.333825758681 0.084775503376
0.24 -0.351966813302 0.039321651365
0.25 -0.365263292116 -0.007015385406
0.26 -0.373479834783 -0.053482650916
0.27 -0.376446054465 -0.099312964922
0.28 -0.374060179266 -0.143736545037
0.29 -0.36629196109 -0.185992995666
0.3 -0.353184793932 -0.225343511304
0.31 -0.334856989098 -0.261083132681
0.32 -0.311502160944 -0.292552886527
0.33 -0.283388683593 -0.319151633573
0.34 -0.250858186588 -0.34034744483
0.35 -0.214323065725 -0.355688323458
0.36 -0.174262994161 -0.364812088674
0.37 -0.131220428525 -0.367455239443
0.38 -0.085795114939 -0.363460619061
0.39 -0.038637610727 -0.352783707554
0.4 0.009558151015 -0.335497376964
0.41 0.05806321482 -0.311794955342
0.42 0.106122822567 -0.281991458627
0.43 0.152966434941 -0.246522865679
0.44 0.197818476692 -0.205943330604
0.45 0.239909714079 -0.16092024823
0.46 0.278489158926 -0.112227113178
0.47 0.312836379591 -0.060734140456
0.48 0.342274084898 -0.007396645852
0.49 0.366180832865 0.046758782371
0.5 0.384003701959 0.100650253017
0.51 0.395270748723 0.1531585766
0.52 0.399603062177 0.203147157716
0.53 0.396726212444 0.249483584201
0.54 0.386480878848 0.291062676372
0.55 0.368832431458 0.326830711984
0.56 0.343879229864 0.355810493373
0.57 0.311859394248 0.377126872844
0.58 0.273155796651 0.390032301305
0.59 0.228299015229 0.393931913926
0.6 0.177967991447 0.388407615826
0.61 0.122988130025 0.373240581299
0.62 0.064326584529 0.348431532667
0.63 0.003084478165 0.314218120551
0.64 -0.059514179679 0.27108868736
0.65 -0.122137104715 0.219791661428
0.66 -0.183362078841 0.161339802162
0.67 -0.241699194812 0.09700849855
0.68 -0.295617142362 0.028327316677
0.69 -0.343573628854 -0.042936000997
0.7 -0.384049972246 -0.114799857912
0.71 -0.415589836646 -0.185102176191
0.72 -0.436841998821 -0.251543479905
0.73 -0.446606934939 -0.311740249958
0.74 -0.443886897333 -0.36328897694
0.75 -0.42793900698 -0.403841159768
0.76 -0.398330713364 -0.431189266299
0.77 -0.354996762639 -0.443363375442
0.78 -0.298296558657 -0.438737843451
0.79 -0.229070487601 -0.416146860569
0.8 -0.148693389774 -0.375007162373
0.81 -0.059122879674 -0.315445398693
0.82 0.037060392906 -0.238426695237
0.83 0.136624226105 -0.14587970383
0.84 0.235672791066 -0.040811833611
0.85 0.329657038947 0.072593748438
0.86 0.413415452061 0.188910568782
0.87 0.481255540298 0.30144580595
0.88 0.527090131457 0.402282185944
0.89 0.544647931947 0.482413021831
0.9 0.527786247319 0.532010304529
0.91 0.470947425343 0.540884181795
0.92 0.36982407832 0.499222843772
0.93 0.222341272749 0.398756426547
0.94 0.030149676775 0.234593905049
0.95 -0.198987710628 0.008206944663
0.96 -0.447060741482 -0.267417856663
0.97 -0.677666883456 -0.557846525986
0.98 -0.816134849434 -0.78386649704
0.99 -0.67654202792 -0.740108414035
0.9999999999 8.839621604036 8.756288259545







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