Legendre.java running P[2][0]=-0.5 P[2][1]=0.0 P[2][2]=1.5 P[3][0]=-0.0 P[3][1]=-1.5 P[3][2]=0.0 P[3][3]=2.5 P[4][0]=0.375 P[4][1]=-0.0 P[4][2]=-3.75 P[4][3]=0.0 P[4][4]=4.375 P[5][0]=0.0 P[5][1]=1.8750000000000002 P[5][2]=-0.0 P[5][3]=-8.75 P[5][4]=0.0 P[5][5]=7.875 P[6][0]=-0.3125 P[6][1]=0.0 P[6][2]=6.5625 P[6][3]=-0.0 P[6][4]=-19.687499999999996 P[6][5]=0.0 P[6][6]=14.4375 P[7][0]=-0.0 P[7][1]=-2.1875 P[7][2]=0.0 P[7][3]=19.6875 P[7][4]=-0.0 P[7][5]=-43.31249999999999 P[7][6]=0.0 P[7][7]=26.8125 P[8][0]=0.2734375 P[8][1]=-0.0 P[8][2]=-9.84375 P[8][3]=0.0 P[8][4]=54.140625 P[8][5]=-0.0 P[8][6]=-93.84374999999999 P[8][7]=0.0 P[8][8]=50.2734375 P[9][0]=0.0 P[9][1]=2.4609375 P[9][2]=-0.0 P[9][3]=-36.09375 P[9][4]=0.0 P[9][5]=140.765625 P[9][6]=-0.0 P[9][7]=-201.09374999999997 P[9][8]=0.0 P[9][9]=94.9609375 P[10][0]=-0.24609375 P[10][1]=0.0 P[10][2]=13.53515625 P[10][3]=-0.0 P[10][4]=-117.3046875 P[10][5]=0.0 P[10][6]=351.9140625 P[10][7]=-0.0 P[10][8]=-427.32421874999994 P[10][9]=0.0 P[10][10]=180.42578125 P[11][0]=-0.0 P[11][1]=-2.70703125 P[11][2]=0.0 P[11][3]=58.65234375 P[11][4]=-0.0 P[11][5]=-351.9140625 P[11][6]=0.0 P[11][7]=854.6484375 P[11][8]=-0.0 P[11][9]=-902.1289062499999 P[11][10]=0.0 P[11][11]=344.44921875 P[12][0]=0.2255859375 P[12][1]=-0.0 P[12][2]=-17.595703125 P[12][3]=0.0 P[12][4]=219.9462890625 P[12][5]=-0.0 P[12][6]=-997.08984375 P[12][7]=0.0 P[12][8]=2029.7900390625 P[12][9]=-0.0 P[12][10]=-1894.470703125 P[12][11]=0.0 P[12][12]=660.1943359375 P[13][0]=0.0 P[13][1]=2.9326171875 P[13][2]=-0.0 P[13][3]=-87.978515625 P[13][4]=0.0 P[13][5]=747.8173828125 P[13][6]=-0.0 P[13][7]=-2706.38671875 P[13][8]=0.0 P[13][9]=4736.1767578125 P[13][10]=-0.0 P[13][11]=-3961.166015625 P[13][12]=0.0 P[13][13]=1269.6044921875 P[14][0]=-0.20947265625 P[14][1]=0.0 P[14][2]=21.99462890625 P[14][3]=-0.0 P[14][4]=-373.90869140625 P[14][5]=0.0 P[14][6]=2368.08837890625 P[14][7]=-0.0 P[14][8]=-7104.26513671875 P[14][9]=0.0 P[14][10]=10893.20654296875 P[14][11]=-0.0 P[14][12]=-8252.42919921875 P[14][13]=0.0 P[14][14]=2448.52294921875 P[15][0]=-0.0 P[15][1]=-3.14208984375 P[15][2]=0.0 P[15][3]=124.63623046875 P[15][4]=-0.0 P[15][5]=-1420.85302734375 P[15][6]=0.0 P[15][7]=7104.26513671875 P[15][8]=-0.0 P[15][9]=-18155.34423828125 P[15][10]=0.0 P[15][11]=24757.28759765625 P[15][12]=-0.0 P[15][13]=-17139.66064453125 P[15][14]=0.0 P[15][15]=4733.81103515625 DP[1][0]=1.0 DP[2][0]=0.0 DP[2][1]=3.0 DP[3][0]=-1.5 DP[3][1]=0.0 DP[3][2]=7.5 DP[4][0]=-0.0 DP[4][1]=-7.5 DP[4][2]=0.0 DP[4][3]=17.5 DP[5][0]=1.8750000000000002 DP[5][1]=-0.0 DP[5][2]=-26.25 DP[5][3]=0.0 DP[5][4]=39.375 DP[6][0]=0.0 DP[6][1]=13.125 DP[6][2]=-0.0 DP[6][3]=-78.74999999999999 DP[6][4]=0.0 DP[6][5]=86.625 DP[7][0]=-2.1875 DP[7][1]=0.0 DP[7][2]=59.0625 DP[7][3]=-0.0 DP[7][4]=-216.56249999999997 DP[7][5]=0.0 DP[7][6]=187.6875 DP[8][0]=-0.0 DP[8][1]=-19.6875 DP[8][2]=0.0 DP[8][3]=216.5625 DP[8][4]=-0.0 DP[8][5]=-563.0624999999999 DP[8][6]=0.0 DP[8][7]=402.1875 DP[9][0]=2.4609375 DP[9][1]=-0.0 DP[9][2]=-108.28125 DP[9][3]=0.0 DP[9][4]=703.828125 DP[9][5]=-0.0 DP[9][6]=-1407.6562499999998 DP[9][7]=0.0 DP[9][8]=854.6484375 DP[10][0]=0.0 DP[10][1]=27.0703125 DP[10][2]=-0.0 DP[10][3]=-469.21875 DP[10][4]=0.0 DP[10][5]=2111.484375 DP[10][6]=-0.0 DP[10][7]=-3418.5937499999995 DP[10][8]=0.0 DP[10][9]=1804.2578125 DP[11][0]=-2.70703125 DP[11][1]=0.0 DP[11][2]=175.95703125 DP[11][3]=-0.0 DP[11][4]=-1759.5703125 DP[11][5]=0.0 DP[11][6]=5982.5390625 DP[11][7]=-0.0 DP[11][8]=-8119.160156249999 DP[11][9]=0.0 DP[11][10]=3788.94140625 DP[12][0]=-0.0 DP[12][1]=-35.19140625 DP[12][2]=0.0 DP[12][3]=879.78515625 DP[12][4]=-0.0 DP[12][5]=-5982.5390625 DP[12][6]=0.0 DP[12][7]=16238.3203125 DP[12][8]=-0.0 DP[12][9]=-18944.70703125 DP[12][10]=0.0 DP[12][11]=7922.33203125 DP[13][0]=2.9326171875 DP[13][1]=-0.0 DP[13][2]=-263.935546875 DP[13][3]=0.0 DP[13][4]=3739.0869140625 DP[13][5]=-0.0 DP[13][6]=-18944.70703125 DP[13][7]=0.0 DP[13][8]=42625.5908203125 DP[13][9]=-0.0 DP[13][10]=-43572.826171875 DP[13][11]=0.0 DP[13][12]=16504.8583984375 DP[14][0]=0.0 DP[14][1]=43.9892578125 DP[14][2]=-0.0 DP[14][3]=-1495.634765625 DP[14][4]=0.0 DP[14][5]=14208.5302734375 DP[14][6]=-0.0 DP[14][7]=-56834.12109375 DP[14][8]=0.0 DP[14][9]=108932.0654296875 DP[14][10]=-0.0 DP[14][11]=-99029.150390625 DP[14][12]=0.0 DP[14][13]=34279.3212890625 R[2][0]=0.5773502691896257 R[2][1]=-0.5773502691896257 R[3][0]=0.0 R[3][1]=0.7745966692414834 R[3][2]=-0.7745966692414834 R[4][0]=0.8611363115940526 R[4][1]=-0.8611363115940526 R[4][2]=0.3399810435848563 R[4][3]=-0.3399810435848563 R[5][0]=0.0 R[5][1]=0.906179845938664 R[5][2]=-0.906179845938664 R[5][3]=0.5384693101056831 R[5][4]=-0.5384693101056831 R[6][0]=0.9324695142031518 R[6][1]=-0.9324695142031518 R[6][2]=0.6612093864662646 R[6][3]=-0.6612093864662646 R[6][4]=0.23861918608319704 R[6][5]=-0.23861918608319704 R[7][0]=0.0 R[7][1]=0.9491079123427583 R[7][2]=-0.9491079123427583 R[7][3]=0.7415311855993942 R[7][4]=-0.7415311855993942 R[7][5]=0.40584515137739774 R[7][6]=-0.40584515137739774 R[8][0]=0.9602898564975352 R[8][1]=-0.9602898564975352 R[8][2]=0.7966664774136283 R[8][3]=-0.7966664774136283 R[8][4]=0.525532409916328 R[8][5]=-0.525532409916328 R[8][6]=0.18343464249565078 R[8][7]=-0.18343464249565078 R[9][0]=0.0 R[9][1]=0.9681602395076243 R[9][2]=-0.9681602395076243 R[9][3]=0.8360311073266388 R[9][4]=-0.8360311073266388 R[9][5]=0.6133714327005877 R[9][6]=-0.6133714327005877 R[9][7]=0.32425342340381097 R[9][8]=-0.32425342340381097 R[10][0]=0.9739065285171717 R[10][1]=-0.9739065285171717 R[10][2]=0.8650633666889799 R[10][3]=-0.8650633666889799 R[10][4]=0.6794095682990379 R[10][5]=-0.6794095682990379 R[10][6]=0.43339539412922734 R[10][7]=-0.43339539412922734 R[10][8]=0.14887433898165375 R[10][9]=-0.14887433898165375 R[11][0]=0.0 R[11][1]=0.978228658146052 R[11][2]=-0.978228658146052 R[11][3]=0.8870625997681049 R[11][4]=-0.8870625997681049 R[11][5]=0.7301520055740407 R[11][6]=-0.7301520055740407 R[11][7]=0.5190961292068189 R[11][8]=-0.5190961292068189 R[11][9]=0.2695431559523407 R[11][10]=-0.2695431559523407 R[12][0]=0.9815606342467192 R[12][1]=-0.9815606342467192 R[12][2]=0.9041172563704739 R[12][3]=-0.9041172563704739 R[12][4]=0.7699026741943049 R[12][5]=-0.7699026741943049 R[12][6]=0.5873179542866226 R[12][7]=-0.5873179542866226 R[12][8]=0.3678314989981681 R[12][9]=-0.3678314989981681 R[12][10]=0.12523340851148568 R[12][11]=-0.12523340851148568 R[13][0]=0.0 R[13][1]=0.984183054718583 R[13][2]=-0.984183054718583 R[13][3]=0.9175983992230051 R[13][4]=-0.9175983992230051 R[13][5]=0.8015780907332498 R[13][6]=-0.8015780907332498 R[13][7]=0.6423493394404203 R[13][8]=-0.6423493394404203 R[13][9]=0.4484927510363726 R[13][10]=-0.4484927510363726 R[13][11]=0.2304583159551792 R[13][12]=-0.2304583159551792 R[14][0]=0.9862838086968059 R[14][1]=-0.9862838086968059 R[14][2]=0.9284348836636057 R[14][3]=-0.9284348836636057 R[14][4]=0.8272013150696949 R[14][5]=-0.8272013150696949 R[14][6]=0.6872929048117841 R[14][7]=-0.6872929048117841 R[14][8]=0.5152486363580419 R[14][9]=-0.5152486363580419 R[14][10]=0.3191123689280062 R[14][11]=-0.3191123689280062 R[14][12]=0.10805494870722726 R[14][13]=-0.10805494870722726 W[2][0]=1.0 W[2][1]=1.0 sum W=2.0 W[3][0]=0.8888888888888888 W[3][1]=0.5555555555555558 W[3][2]=0.5555555555555558 sum W=2.0000000000000004 W[4][0]=0.3478548451374539 W[4][1]=0.3478548451374539 W[4][2]=0.652145154862546 W[4][3]=0.652145154862546 sum W=1.9999999999999996 W[5][0]=0.5688888888888888 W[5][1]=0.23692688505619144 W[5][2]=0.23692688505619144 W[5][3]=0.4786286704993662 W[5][4]=0.4786286704993662 sum W=2.000000000000004 W[6][0]=0.17132449237917324 W[6][1]=0.17132449237917324 W[6][2]=0.36076157304813755 W[6][3]=0.36076157304813755 W[6][4]=0.46791393457269115 W[6][5]=0.46791393457269115 sum W=2.0000000000000036 W[7][0]=0.4179591836734694 W[7][1]=0.12948496616887303 W[7][2]=0.12948496616887303 W[7][3]=0.2797053914892715 W[7][4]=0.2797053914892715 W[7][5]=0.38183005050511964 W[7][6]=0.38183005050511964 sum W=1.9999999999999978 W[8][0]=0.10122853629038456 W[8][1]=0.10122853629038456 W[8][2]=0.22238103445337304 W[8][3]=0.22238103445337304 W[8][4]=0.3137066458778861 W[8][5]=0.3137066458778861 W[8][6]=0.36268378337836243 W[8][7]=0.36268378337836243 sum W=2.0000000000000124 W[9][0]=0.3302393550012598 W[9][1]=0.08127438836159948 W[9][2]=0.08127438836159948 W[9][3]=0.1806481606948691 W[9][4]=0.1806481606948691 W[9][5]=0.26061069640293194 W[9][6]=0.26061069640293194 W[9][7]=0.3123470770400047 W[9][8]=0.3123470770400047 sum W=2.00000000000007 W[10][0]=0.06667134430867126 W[10][1]=0.06667134430867126 W[10][2]=0.14945134915054867 W[10][3]=0.14945134915054867 W[10][4]=0.21908636251602195 W[10][5]=0.21908636251602195 W[10][6]=0.2692667193099704 W[10][7]=0.2692667193099704 W[10][8]=0.29552422471476203 W[10][9]=0.29552422471476203 sum W=1.9999999999999487 W[11][0]=0.2729250867779006 W[11][1]=0.05566856711614893 W[11][2]=0.05566856711614893 W[11][3]=0.12558036946493734 W[11][4]=0.12558036946493734 W[11][5]=0.18629021092769588 W[11][6]=0.18629021092769588 W[11][7]=0.23319376459200086 W[11][8]=0.23319376459200086 W[11][9]=0.26280454451024315 W[11][10]=0.26280454451024315 sum W=1.9999999999999527 W[12][0]=0.04717533638672337 W[12][1]=0.04717533638672337 W[12][2]=0.10693932599527142 W[12][3]=0.10693932599527142 W[12][4]=0.16007832854335757 W[12][5]=0.16007832854335757 W[12][6]=0.20316742672307395 W[12][7]=0.20316742672307395 W[12][8]=0.23349253653834146 W[12][9]=0.23349253653834146 W[12][10]=0.2491470458134086 W[12][11]=0.2491470458134086 sum W=2.0000000000003526 W[13][0]=0.2325515532308739 W[13][1]=0.04048400476552451 W[13][2]=0.04048400476552451 W[13][3]=0.09212149983797953 W[13][4]=0.09212149983797953 W[13][5]=0.13887351021950273 W[13][6]=0.13887351021950273 W[13][7]=0.17814598076214724 W[13][8]=0.17814598076214724 W[13][9]=0.20781604753678318 W[13][10]=0.20781604753678318 W[13][11]=0.22628318026292657 W[13][12]=0.22628318026292657 sum W=2.0000000000006013 W[14][0]=0.03511946033221103 W[14][1]=0.03511946033221103 W[14][2]=0.08015808716050249 W[14][3]=0.08015808716050249 W[14][4]=0.12151857068751033 W[14][5]=0.12151857068751033 W[14][6]=0.15720316715841032 W[14][7]=0.15720316715841032 W[14][8]=0.18553839747775105 W[14][9]=0.18553839747775105 W[14][10]=0.20519846372140604 W[14][11]=0.20519846372140604 W[14][12]=0.21526385346312216 W[14][13]=0.21526385346312216 sum W=2.0000000000018265 Gauss-Legendre quadrature of e^x from 1.0 to 3.0 = 17.367255094728623 n=2 approx=17.310312816310372 err=0.05694227841825139 n=3 approx=17.366771417404976 err=4.8367732364695826E-4 n=4 approx=17.36725291398744 err=2.180741184076851E-6 n=5 approx=17.367255088634344 err=6.094278859336555E-9 n=6 approx=17.367255094717077 err=1.1546319456101628E-11 n=7 approx=17.367255094728595 err=2.8421709430404007E-14 n=8 approx=17.367255094728762 err=-1.3855583347321954E-13 n=9 approx=17.367255094729387 err=-7.638334409421077E-13 n=10 approx=17.367255094728034 err=5.897504706808832E-13 n=11 approx=17.36725509472815 err=4.725109192804666E-13 n=12 approx=17.367255094732617 err=-3.993250174971763E-12 n=13 approx=17.367255094735427 err=-6.803446694902959E-12 n=14 approx=17.36725509474916 err=-2.0538237777145696E-11