Formelsammlung Mathematik: Tabellen: Gauß-Legendre-Quadratur

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Die Tabellen sind von der Form (ein n-Tupel von geordneten Paaren), wobei das Gewicht zur Stützstelle ist.

[1][Bearbeiten]

tableGL1 = [
  [0.0, 2.0]
]

[2][Bearbeiten]

tableGL2 = [
  [-0.5773502691896257, 1.0],
  [ 0.5773502691896257, 1.0]
]

[3][Bearbeiten]

tableGL3 = [
  [-0.7745966692414834, 0.5555555555555554],
  [ 0.0000000000000000, 0.8888888888888888],
  [ 0.7745966692414834, 0.5555555555555554]
]

[4][Bearbeiten]

tableGL4 = [
  [-0.8611363115940527, 0.3478548451374536],
  [-0.3399810435848563, 0.6521451548625462],
  [ 0.3399810435848563, 0.6521451548625462],
  [ 0.8611363115940527, 0.3478548451374536]
]

[5][Bearbeiten]

tableGL5 = [
  [-0.9061798459386641, 0.2369268850561889],
  [-0.5384693101056830, 0.4786286704993666],
  [ 0.0000000000000000, 0.5688888888888889],
  [ 0.5384693101056830, 0.4786286704993666],
  [ 0.9061798459386641, 0.2369268850561889]
]

[6][Bearbeiten]

tableGL6 = [
  [-0.9324695142031521, 0.1713244923791704],
  [-0.6612093864662645, 0.3607615730481387],
  [-0.2386191860831969, 0.4679139345726913],
  [ 0.2386191860831969, 0.4679139345726913],
  [ 0.6612093864662645, 0.3607615730481387],
  [ 0.9324695142031521, 0.1713244923791704]
]

[7][Bearbeiten]

tableGL7 = [
  [-0.9491079123427586, 0.1294849661688695],
  [-0.7415311855993945, 0.2797053914892767],
  [-0.4058451513773972, 0.3818300505051189],
  [ 0.0000000000000000, 0.4179591836734694],
  [ 0.4058451513773972, 0.3818300505051189],
  [ 0.7415311855993945, 0.2797053914892767],
  [ 0.9491079123427586, 0.1294849661688695]
]

[8][Bearbeiten]

tableGL8 = [
  [-0.9602898564975362, 0.1012285362903764],
  [-0.7966664774136267, 0.2223810344533745],
  [-0.5255324099163290, 0.3137066458778874],
  [-0.1834346424956498, 0.3626837833783619],
  [ 0.1834346424956498, 0.3626837833783619],
  [ 0.5255324099163290, 0.3137066458778874],
  [ 0.7966664774136267, 0.2223810344533745],
  [ 0.9602898564975362, 0.1012285362903764]
]

[9][Bearbeiten]

tableGL9 = [
  [-0.9681602395076261, 0.08127438836157445],
  [-0.8360311073266358, 0.1806481606948574],
  [-0.6133714327005904, 0.2606106964029355],
  [-0.3242534234038089, 0.3123470770400029],
  [ 0.0000000000000000, 0.3302393550012598],
  [ 0.3242534234038089, 0.3123470770400029],
  [ 0.6133714327005904, 0.2606106964029355],
  [ 0.8360311073266358, 0.1806481606948574],
  [ 0.9681602395076261, 0.08127438836157445]
]

[10][Bearbeiten]

tableGL10 = [
  [-0.9739065285171717, 0.06667134430868804],
  [-0.8650633666889844, 0.1494513491505807],
  [-0.6794095682990244, 0.2190863625159821],
  [-0.4333953941292472, 0.2692667193099963],
  [-0.1488743389816312, 0.2955242247147528],
  [ 0.1488743389816312, 0.2955242247147528],
  [ 0.4333953941292472, 0.2692667193099963],
  [ 0.6794095682990244, 0.2190863625159821],
  [ 0.8650633666889844, 0.1494513491505807],
  [ 0.9739065285171717, 0.06667134430868804]
]

[11][Bearbeiten]

tableGL11 = [
  [-0.9782286581460571, 0.05566856711617345],
  [-0.8870625997680952, 0.1255803694649047],
  [-0.7301520055740494, 0.1862902109277342],
  [-0.5190961292068119, 0.2331937645919904],
  [-0.2695431559523450, 0.2628045445102466],
  [ 0.0000000000000000, 0.2729250867779006],
  [ 0.2695431559523450, 0.2628045445102466],
  [ 0.5190961292068119, 0.2331937645919904],
  [ 0.7301520055740494, 0.1862902109277342],
  [ 0.8870625997680952, 0.1255803694649047],
  [ 0.9782286581460571, 0.05566856711617345]
]

[12][Bearbeiten]

tableGL12 = [
  [-0.9815606342467191, 0.0471753363865122],
  [-0.9041172563704749, 0.1069393259953184],
  [-0.7699026741943047, 0.1600783285433461],
  [-0.5873179542866174, 0.2031674267230660],
  [-0.3678314989981802, 0.2334925365383548],
  [-0.1252334085114689, 0.2491470458134028],
  [ 0.1252334085114689, 0.2491470458134028],
  [ 0.3678314989981802, 0.2334925365383548],
  [ 0.5873179542866174, 0.2031674267230660],
  [ 0.7699026741943047, 0.1600783285433461],
  [ 0.9041172563704749, 0.1069393259953184],
  [ 0.9815606342467191, 0.0471753363865122]
]

[13][Bearbeiten]

tableGL13 = [
  [-0.9841830547185881, 0.04048400476531590],
  [-0.9175983992229779, 0.09212149983772848],
  [-0.8015780907333099, 0.1388735102197872],
  [-0.6423493394403401, 0.1781459807619458],
  [-0.4484927510364468, 0.2078160475368885],
  [-0.2304583159551348, 0.2262831802628972],
  [ 0.0000000000000000, 0.2325515532308739],
  [ 0.2304583159551348, 0.2262831802628972],
  [ 0.4484927510364468, 0.2078160475368885],
  [ 0.6423493394403401, 0.1781459807619458],
  [ 0.8015780907333099, 0.1388735102197872],
  [ 0.9175983992229779, 0.09212149983772848],
  [ 0.9841830547185881, 0.04048400476531590]
]

[14][Bearbeiten]

tableGL14 = [
  [-0.9862838086968124, 0.03511946033175165],
  [-0.9284348836635736, 0.08015808715976008],
  [-0.8272013150697650, 0.1215185706879031],
  [-0.6872929048116854, 0.1572031671581936],
  [-0.5152486363581541, 0.1855383974779378],
  [-0.3191123689278897, 0.2051984637212955],
  [-0.1080549487073437, 0.2152638534631578],
  [ 0.1080549487073437, 0.2152638534631578],
  [ 0.3191123689278897, 0.2051984637212955],
  [ 0.5152486363581541, 0.1855383974779378],
  [ 0.6872929048116854, 0.1572031671581936],
  [ 0.8272013150697650, 0.1215185706879031],
  [ 0.9284348836635736, 0.08015808715976008],
  [ 0.9862838086968124, 0.03511946033175165]
]

[15][Bearbeiten]

tableGL15 = [
  [-0.9879925180204854, 0.03075324199611744],
  [-0.9372733924007060, 0.0703660474881081],
  [-0.8482065834104273, 0.1071592204671718],
  [-0.7244177313601701, 0.1395706779261544],
  [-0.5709721726085388, 0.1662692058169939],
  [-0.3941513470775634, 0.1861610000155622],
  [-0.2011940939974345, 0.1984314853271116],
  [ 0.0000000000000000, 0.2025782419255613],
  [ 0.2011940939974345, 0.1984314853271116],
  [ 0.3941513470775634, 0.1861610000155622],
  [ 0.5709721726085388, 0.1662692058169939],
  [ 0.7244177313601701, 0.1395706779261544],
  [ 0.8482065834104273, 0.1071592204671718],
  [ 0.9372733924007060, 0.0703660474881081],
  [ 0.9879925180204854, 0.03075324199611744]
]

[16][Bearbeiten]

tableGL16 = [
  [-0.9894009349916499, 0.02715245941175403],
  [-0.9445750230732326, 0.06225352393864787],
  [-0.8656312023878316, 0.09515851168249286],
  [-0.7554044083550031, 0.1246289712555339],
  [-0.6178762444026438, 0.1495959888165767],
  [-0.4580167776572274, 0.1691565193950026],
  [-0.2816035507792589, 0.1826034150449236],
  [-0.09501250983763745,0.1894506104550685],
  [ 0.09501250983763745,0.1894506104550685],
  [ 0.2816035507792589, 0.1826034150449236],
  [ 0.4580167776572274, 0.1691565193950026],
  [ 0.6178762444026438, 0.1495959888165767],
  [ 0.7554044083550031, 0.1246289712555339],
  [ 0.8656312023878316, 0.09515851168249286],
  [ 0.9445750230732326, 0.06225352393864787],
  [ 0.9894009349916499, 0.02715245941175403]
]

[32][Bearbeiten]

tableGL32 = [
  [-0.9972638618494816, 0.007018610009470141],
  [-0.9856115115452684, 0.01627439473090563],
  [-0.9647622555875064, 0.02539206530926208],
  [-0.9349060759377397, 0.03427386291302148],
  [-0.8963211557660522, 0.04283589802222668],
  [-0.8493676137325699, 0.05099805926237622],
  [-0.7944837959679425, 0.05868409347853551],
  [-0.7321821187402897, 0.06582222277636184],
  [-0.6630442669302152, 0.07234579410884850],
  [-0.5877157572407623, 0.07819389578707028],
  [-0.5068999089322295, 0.08331192422694673],
  [-0.4213512761306354, 0.08765209300440380],
  [-0.3318686022821277, 0.09117387869576390],
  [-0.2392873622521371, 0.09384439908080457],
  [-0.1444719615827965, 0.09563872007927489],
  [-0.04830766568773831,0.09654008851472778],
  [ 0.04830766568773831,0.09654008851472778],
  [ 0.1444719615827965, 0.09563872007927489],
  [ 0.2392873622521371, 0.09384439908080457],
  [ 0.3318686022821277, 0.09117387869576390],
  [ 0.4213512761306354, 0.08765209300440380],
  [ 0.5068999089322295, 0.08331192422694673],
  [ 0.5877157572407623, 0.07819389578707028],
  [ 0.6630442669302152, 0.07234579410884850],
  [ 0.7321821187402897, 0.06582222277636184],
  [ 0.7944837959679425, 0.05868409347853551],
  [ 0.8493676137325699, 0.05099805926237622],
  [ 0.8963211557660522, 0.04283589802222668],
  [ 0.9349060759377397, 0.03427386291302148],
  [ 0.9647622555875064, 0.02539206530926208],
  [ 0.9856115115452684, 0.01627439473090563],
  [ 0.9972638618494816, 0.007018610009470141]
]

[64][Bearbeiten]

tableGL64 = [
  [-0.9993050417357721, 0.001783280721696567],
  [-0.9963401167719552, 0.004147033260562497],
  [-0.9910133714767444, 0.006504457968978312],
  [-0.9833362538846260, 0.00884675982636394],
  [-0.9733268277899110, 0.01116813946013113],
  [-0.9610087996520538, 0.01346304789671862],
  [-0.9464113748584029, 0.01572603047602469],
  [-0.9295691721319397, 0.01795171577569731],
  [-0.9105221370785028, 0.02013482315353021],
  [-0.8893154459951140, 0.02227017380838327],
  [-0.8659993981540928, 0.02435270256871088],
  [-0.8406292962525803, 0.02637746971505467],
  [-0.8132653151227975, 0.02833967261425949],
  [-0.7839723589433414, 0.03023465707240245],
  [-0.7528199072605319, 0.03205792835485153],
  [-0.7198818501716109, 0.03380516183714161],
  [-0.6852363130542332, 0.03547221325688238],
  [-0.6489654712546573, 0.03705512854024007],
  [-0.6111553551723932, 0.03855015317861561],
  [-0.5718956462026341, 0.03995374113272036],
  [-0.5312794640198946, 0.04126256324262352],
  [-0.4894031457070530, 0.04247351512365356],
  [-0.4463660172534641, 0.04358372452932344],
  [-0.4022701579639916, 0.04459055816375653],
  [-0.3572201583376681, 0.04549162792741817],
  [-0.3113228719902109, 0.04628479658131444],
  [-0.2646871622087674, 0.04696818281621003],
  [-0.2174236437400071, 0.04754016571483032],
  [-0.1696444204239928, 0.04799938859645833],
  [-0.1214628192961205, 0.04834476223480293],
  [-0.07299312178779904,0.04857546744150344],
  [-0.02435029266342443,0.04869095700913968],
  [ 0.02435029266342443,0.04869095700913968],
  [ 0.07299312178779904,0.04857546744150344],
  [ 0.1214628192961205, 0.04834476223480293],
  [ 0.1696444204239928, 0.04799938859645833],
  [ 0.2174236437400071, 0.04754016571483032],
  [ 0.2646871622087674, 0.04696818281621003],
  [ 0.3113228719902109, 0.04628479658131444],
  [ 0.3572201583376681, 0.04549162792741817],
  [ 0.4022701579639916, 0.04459055816375653],
  [ 0.4463660172534641, 0.04358372452932344],
  [ 0.4894031457070530, 0.04247351512365356],
  [ 0.5312794640198946, 0.04126256324262352],
  [ 0.5718956462026341, 0.03995374113272036],
  [ 0.6111553551723932, 0.03855015317861561],
  [ 0.6489654712546573, 0.03705512854024007],
  [ 0.6852363130542332, 0.03547221325688238],
  [ 0.7198818501716109, 0.03380516183714161],
  [ 0.7528199072605319, 0.03205792835485153],
  [ 0.7839723589433414, 0.03023465707240245],
  [ 0.8132653151227975, 0.02833967261425949],
  [ 0.8406292962525803, 0.02637746971505467],
  [ 0.8659993981540928, 0.02435270256871088],
  [ 0.8893154459951140, 0.02227017380838327],
  [ 0.9105221370785028, 0.02013482315353021],
  [ 0.9295691721319397, 0.01795171577569731],
  [ 0.9464113748584029, 0.01572603047602469],
  [ 0.9610087996520538, 0.01346304789671862],
  [ 0.9733268277899110, 0.01116813946013113],
  [ 0.9833362538846260, 0.00884675982636394],
  [ 0.9910133714767444, 0.006504457968978312],
  [ 0.9963401167719552, 0.004147033260562497],
  [ 0.9993050417357721, 0.001783280721696567]
]

[128][Bearbeiten]

tableGL128 = [
  [-0.9998248879471319, 0.0004493809602922304],
  [-0.9990774599773760, 0.001045812679340310],
  [-0.9977332486255139, 0.001642503018669108],
  [-0.9957927585349813, 0.002238288430962588],
  [-0.9932571129002130, 0.002832751471457974],
  [-0.9901278184917344, 0.003425526040910230],
  [-0.9864067427245862, 0.004016254983738653],
  [-0.9820961084357185, 0.004604584256702980],
  [-0.9771984914639074, 0.005190161832676335],
  [-0.9717168187471366, 0.005772637542865690],
  [-0.9656543664319652, 0.006351663161707191],
  [-0.9590147578536998, 0.006926892566898831],
  [-0.9518019613412645, 0.007497981925634717],
  [-0.9440202878302202, 0.008064589890486057],
  [-0.9356743882779164, 0.008626377798616745],
  [-0.9267692508789478, 0.009183009871660886],
  [-0.9173101980809606, 0.009734153415006800],
  [-0.9073028834017569, 0.01027947901583214],
  [-0.8967532880491582, 0.01081866073950309],
  [-0.8856677173453973, 0.01135137632408039],
  [-0.8740527969580318, 0.01187730737274027],
  [-0.8619154689395485, 0.01239613954395092],
  [-0.8492629875779689, 0.01290756273926735],
  [-0.8361029150609069, 0.01341127128861632],
  [-0.8224431169556439, 0.01390696413295199],
  [-0.8082917575079136, 0.01439434500416686],
  [-0.7936572947621934, 0.01487312260214732],
  [-0.7785484755064120, 0.01534301076886515],
  [-0.7629743300440948, 0.01580372865939933],
  [-0.7469441667970620, 0.01625500090978519],
  [-0.7304675667419087, 0.01669655780158921],
  [-0.7135543776835873, 0.01712813542311139],
  [-0.6962147083695143, 0.01754947582711769],
  [-0.6784589224477193, 0.01796032718500867],
  [-0.6602976322726462, 0.01836044393733133],
  [-0.6417416925623076, 0.01874958694054468],
  [-0.6228021939105850, 0.01912752360995093],
  [-0.6034904561585486, 0.01949402805870663],
  [-0.5838180216287632, 0.01984888123283086],
  [-0.5637966482266181, 0.02019187104213003],
  [-0.5434383024128104, 0.02052279248696008],
  [-0.5227551520511755, 0.02084144778075115],
  [-0.5017595591361446, 0.02114764646822136],
  [-0.4804640724041720, 0.02144120553920845],
  [-0.4588814198335522, 0.02172194953805206],
  [-0.4370245010371042, 0.02198971066846049],
  [-0.4149063795522751, 0.02224432889379978],
  [-0.3925402750332675, 0.02248565203274496],
  [-0.3699395553498590, 0.02271353585023644],
  [-0.3471177285976355, 0.02292784414368686],
  [-0.3240884350244134, 0.02312844882438703],
  [-0.3008654388776772, 0.02331522999406275],
  [-0.2774626201779044, 0.02348807601653592],
  [-0.2538939664226944, 0.02364688358444761],
  [-0.2301735642266600, 0.02379155778100340],
  [-0.2063155909020792, 0.02392201213670346],
  [-0.1823343059853372, 0.02403816868102404],
  [-0.1582440427142249, 0.02413995798901928],
  [-0.1340591994611878, 0.02422731922281525],
  [-0.1097942311276437, 0.02430020016797187],
  [-0.08546364050451549,0.02435855726469064],
  [-0.06108196960413957,0.02440235563384958],
  [-0.03666379096873350,0.02443156909785004],
  [-0.01222369896061576,0.02444618019626252],
  [ 0.01222369896061576,0.02444618019626252],
  [ 0.03666379096873350,0.02443156909785004],
  [ 0.06108196960413957,0.02440235563384958],
  [ 0.08546364050451549,0.02435855726469064],
  [ 0.1097942311276437, 0.02430020016797187],
  [ 0.1340591994611878, 0.02422731922281525],
  [ 0.1582440427142249, 0.02413995798901928],
  [ 0.1823343059853372, 0.02403816868102404],
  [ 0.2063155909020792, 0.02392201213670346],
  [ 0.2301735642266600, 0.02379155778100340],
  [ 0.2538939664226944, 0.02364688358444761],
  [ 0.2774626201779044, 0.02348807601653592],
  [ 0.3008654388776772, 0.02331522999406275],
  [ 0.3240884350244134, 0.02312844882438703],
  [ 0.3471177285976355, 0.02292784414368686],
  [ 0.3699395553498590, 0.02271353585023644],
  [ 0.3925402750332675, 0.02248565203274496],
  [ 0.4149063795522751, 0.02224432889379978],
  [ 0.4370245010371042, 0.02198971066846049],
  [ 0.4588814198335522, 0.02172194953805206],
  [ 0.4804640724041720, 0.02144120553920845],
  [ 0.5017595591361446, 0.02114764646822136],
  [ 0.5227551520511755, 0.02084144778075115],
  [ 0.5434383024128104, 0.02052279248696008],
  [ 0.5637966482266181, 0.02019187104213003],
  [ 0.5838180216287632, 0.01984888123283086],
  [ 0.6034904561585486, 0.01949402805870663],
  [ 0.6228021939105850, 0.01912752360995093],
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