Formelsammlung Mathematik: Tabellen: Gauß-Legendre-Quadratur
Die Tabellen sind von der Form (ein n-Tupel von geordneten Paaren), wobei das Gewicht zur Stützstelle ist.
![{\displaystyle [[x_{i},w_{i}]]_{i=0}^{n-1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e2c1a4f8113d8d3bd07c0ae1642538cc9c909bb)
[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], [ 0.6417416925623076, 0.01874958694054468], [ 0.6602976322726462, 0.01836044393733133], [ 0.6784589224477193, 0.01796032718500867], [ 0.6962147083695143, 0.01754947582711769], [ 0.7135543776835873, 0.01712813542311139], [ 0.7304675667419087, 0.01669655780158921], [ 0.7469441667970620, 0.01625500090978519], [ 0.7629743300440948, 0.01580372865939933], [ 0.7785484755064120, 0.01534301076886515], [ 0.7936572947621934, 0.01487312260214732], [ 0.8082917575079136, 0.01439434500416686], [ 0.8224431169556439, 0.01390696413295199], [ 0.8361029150609069, 0.01341127128861632], [ 0.8492629875779689, 0.01290756273926735], [ 0.8619154689395485, 0.01239613954395092], [ 0.8740527969580318, 0.01187730737274027], [ 0.8856677173453973, 0.01135137632408039], [ 0.8967532880491582, 0.01081866073950309], [ 0.9073028834017569, 0.01027947901583214], [ 0.9173101980809606, 0.009734153415006800], [ 0.9267692508789478, 0.009183009871660886], [ 0.9356743882779164, 0.008626377798616745], [ 0.9440202878302202, 0.008064589890486057], [ 0.9518019613412645, 0.007497981925634717], [ 0.9590147578536998, 0.006926892566898831], [ 0.9656543664319652, 0.006351663161707191], [ 0.9717168187471366, 0.005772637542865690], [ 0.9771984914639074, 0.005190161832676335], [ 0.9820961084357185, 0.004604584256702980], [ 0.9864067427245862, 0.004016254983738653], [ 0.9901278184917344, 0.003425526040910230], [ 0.9932571129002130, 0.002832751471457974], [ 0.9957927585349813, 0.002238288430962588], [ 0.9977332486255139, 0.001642503018669108], [ 0.9990774599773760, 0.001045812679340310], [ 0.9998248879471319, 0.0004493809602922304] ]