Rule: Q[2, 6, 23, 32]

Type

This rule is of Legendre type.

Polynomials

One starts from the polynomial P1 and extends one by one with Pi until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

Node locations in the complex plane

Plot of the node locations in the complex plane.

Magnitude of the Weights

Logarithmic magnitude of the weights
         plotted against the (real part) of the nodes.

Quadrature Rule Data

Nodes

Node (ball center) Error (ball radius)
0.98219129046748981137 + 1.2175014783784493791e-894j 9.59e-233, 9.59e-233j
-0.95704103125552124278 - 8.3916697881861199027e-893j 8.61e-233, 8.61e-233j
-0.94117082451224482217 + 9.2354433120014623926e-906j 7.56e-233, 7.56e-233j
-0.98219129046748981137 + 1.9790695037296128598e-920j 9.89e-233, 9.89e-233j
0.9235173672435537034 + 1.6013159078110586689e-936j 6.21e-233, 6.21e-233j
0.90512404626326724496 - 1.005568944484283544e-936j 5.03e-233, 5.03e-233j
0.99942621346196119044 - 1.7718449701416270736e-936j 2.11e-233, 2.11e-233j
-0.88848227691311736826 + 5.4350185450783568983e-935j 3.42e-233, 3.42e-233j
0.99086118219405337248 + 2.4237017528391867321e-939j 8.21e-233, 8.21e-233j
-0.99659184789930772401 - 2.0006161619763677086e-943j 5.72e-233, 5.72e-233j
0.88848227691311736826 - 1.3357960881743162498e-959j 3.38e-233, 3.38e-233j
0.99659184789930772401 - 1.6132416342421231432e-959j 5.94e-233, 5.94e-233j
-0.9235173672435537034 - 3.4221113885238159644e-959j 6.48e-233, 6.48e-233j
-0.8718828771615970384 - 3.5804653330118970376e-964j 1.67e-233, 1.67e-233j
-0.99086118219405337248 + 1.5175375893629448115e-970j 8.44e-233, 8.44e-233j
0.82660600059929767756 - 9.8986982112913396372e-985j 9.05e-235, 9.05e-235j
0.85110112875893547946 - 3.2821830924351654523e-985j 4.32e-234, 4.32e-234j
-0.99942621346196119044 + 6.0531081519623205801e-981j 2.29e-233, 2.29e-233j
-0.76716360981913079608 + 2.2501522136415903619e-995j 2.76e-236, 2.76e-236j
-0.90512404626326724496 - 3.3574306681919903776e-992j 5.06e-233, 5.06e-233j
0.95704103125552124278 - 6.7074919236703859331e-993j 8.87e-233, 8.87e-233j
0.79851078578936840599 - 3.2909714517805518278e-997j 1.58e-235, 1.58e-235j
0.94117082451224482217 + 9.2277802655383892848e-994j 7.36e-233, 7.36e-233j
-0.79851078578936840599 + 1.3552016270446072001e-997j 1.62e-235, 1.62e-235j
-0.82660600059929767756 - 1.115583233522487094e-996j 9.24e-235, 9.24e-235j
0.8718828771615970384 + 2.1352872964265382282e-996j 1.57e-233, 1.57e-233j
0.6969349108965792951 + 3.7352726371826154669e-1002j 4.77e-238, 4.77e-238j
0.73315618267263425483 - 2.4909471928631687162e-1001j 3.55e-237, 3.55e-237j
-0.49030793160413410634 - 1.8867976806460177594e-1006j 5.32e-243, 5.32e-243j
-0.65876972049695109442 + 8.5610649527375210285e-1002j 5.64e-239, 5.64e-239j
0.97081045978202683917 + 4.0509206693856350107e-997j 9.67e-233, 9.67e-233j
0.76716360981913079608 - 3.4067630585703318302e-1001j 2.32e-236, 2.32e-236j
0.65876972049695109442 + 5.1591760406867317053e-1004j 5.84e-239, 5.84e-239j
-0.97081045978202683917 - 2.15883266593305529e-999j 9.81e-233, 9.81e-233j
-0.6969349108965792951 - 9.3650497652717278463e-1009j 4.78e-238, 4.78e-238j
-0.73315618267263425483 + 1.389281756919014369e-1007j 3.86e-237, 3.86e-237j
0.25401995009868148583 - 1.1466563033420242888e-1022j 4.54e-249, 4.54e-249j
0.61884815471211880181 - 5.1227513803903493425e-1014j 7.08e-240, 7.08e-240j
0.30309200782089397844 + 1.4556214172884662102e-1021j 8.94e-248, 8.94e-248j
-0.85110112875893547946 - 3.7040190171609168552e-1018j 4.32e-234, 4.32e-234j
-0.53445479299468978285 + 8.2482438770094285957e-1026j 6.12e-242, 6.12e-242j
-0.15373890228994365251 + 7.5267654778593598967e-1038j 1.09e-251, 1.09e-251j
0.57735026918962576451 + 4.134495101926970071e-1027j 6.3e-241, 6.3e-241j
0.53445479299468978285 + 8.6126140457134037392e-1029j 5.93e-242, 5.93e-242j
-1.2837034595611786934e-1065 - 3.3171616392933528909e-1065j 2.24e-1063, 2.24e-1063j
-0.57735026918962576451 - 2.9571525223062228168e-1024j 6.37e-241, 6.37e-241j
-0.61884815471211880181 - 5.4219749857733363763e-1031j 6.32e-240, 6.32e-240j
0.051482423679125852868 - 1.5580539714346085014e-1045j 2.03e-254, 2.03e-254j
0.49030793160413410634 - 1.1160734252897702847e-1035j 5.16e-243, 5.16e-243j
0.2041968861768067152 + 1.2225188021925685182e-1043j 2.49e-250, 2.49e-250j
-0.30309200782089397844 - 7.8017673962379828263e-1040j 8.82e-248, 8.82e-248j
-0.4450143285025174533 + 3.2506743962128556938e-1035j 3.89e-244, 3.89e-244j
-0.051482423679125852868 + 2.0146250920758223804e-1045j 2.46e-254, 2.46e-254j
0.3513279806356832542 - 7.6892295450875325335e-1039j 1.58e-246, 1.58e-246j
0.4450143285025174533 + 6.226571010140577616e-1037j 3.86e-244, 3.86e-244j
-0.10278397627077407171 - 3.1898764401944441628e-1044j 4.94e-253, 4.94e-253j
-0.39866002823183718606 + 3.4532342910898417085e-1038j 2.49e-245, 2.49e-245j
-0.25401995009868148583 + 5.0327384481680911958e-1040j 5.05e-249, 5.05e-249j
0.15373890228994365251 - 5.2334006483834209269e-1044j 1.15e-251, 1.15e-251j
0.39866002823183718606 + 2.9649505848910536908e-1038j 2.77e-245, 2.77e-245j
0.10278397627077407171 + 4.7333241281067389373e-1044j 4.87e-253, 4.87e-253j
-0.2041968861768067152 - 1.6437951466780373995e-1041j 2.42e-250, 2.42e-250j
-0.3513279806356832542 - 1.8487600290606708522e-1039j 1.55e-246, 1.55e-246j

Weights

Weight (ball center) Error (ball radius)
0.010075692314228976886 - 6.7405027466160899568e-895j 4.63e-31, 1.39e-141j
0.014860881408103631928 - 4.0321150450913319273e-893j 2.23e-31, 6.72e-142j
0.016837441583577396723 + 1.3864583274788766338e-892j 1.77e-31, 5.31e-142j
0.010075692314228976886 + 1.7312787661296381418e-893j 4.7e-32, 1.41e-142j
0.018322817352656935069 - 4.1399438050185816757e-894j 8.04e-33, 2.42e-143j
0.017962110032012576385 + 7.1683957450032634038e-894j 6.69e-33, 2.01e-143j
0.0015358794360654312006 - 5.2336154516499438764e-896j 3.22e-34, 9.67e-145j
0.015541534980177963612 - 1.7838984250225754693e-892j 3.11e-35, 9.35e-146j
0.0072238105237716463148 - 7.1773283637271354049e-895j 2.86e-34, 8.61e-145j
0.0042378999571021552021 + 3.6526197525468310469e-894j 2.22e-36, 6.66e-147j
0.015541534980177963612 - 1.0291938967033374997e-893j 1.66e-35, 5e-146j
0.0042378999571021552021 + 2.0869741243065245761e-895j 3.04e-34, 9.14e-145j
0.018322817352656935069 - 1.2211969196362181768e-892j 5.2e-36, 1.56e-146j
0.018606248242616986286 + 1.4455653489413924156e-892j 5.92e-37, 1.78e-147j
0.0072238105237716463148 - 7.7557126218540145135e-894j 2.67e-36, 8.02e-147j
0.026303249553207721222 + 4.4668494061662265032e-894j 6.33e-39, 1.9e-149j
0.022714653977741888504 - 6.8760414391954295532e-894j 2.19e-38, 6.6e-149j
0.0015358794360654312006 - 1.0989304039397185961e-894j 4.05e-37, 1.22e-147j
0.032769165155848433568 + 1.5543671817278713213e-893j 4.35e-41, 1.31e-151j
0.017962110032012576385 + 1.5311900383006870793e-892j 2.74e-37, 8.22e-148j
0.014860881408103631928 - 2.0479879106032709747e-894j 1.52e-39, 4.58e-150j
0.029819820860933317103 - 2.9524663664257159361e-894j 7.1e-42, 2.14e-152j
0.016837441583577396723 + 2.6692046483710961416e-894j 2.04e-39, 6.13e-150j
0.029819820860933317103 - 2.582579701155247167e-893j 1.65e-42, 4.95e-153j
0.026303249553207721222 + 4.6268147924968575203e-893j 5.41e-42, 1.63e-152j
0.018606248242616986286 + 9.8609921979332094055e-894j 1.56e-40, 4.68e-151j
0.037227889108837432398 + 1.33977756700698664e-894j 7.89e-46, 2.37e-156j
0.035171528625758069638 - 1.6139539461673402693e-894j 3.45e-45, 1.04e-155j
0.044735163426795916527 - 2.8217122808813681468e-894j 2.69e-50, 8.07e-161j
0.039072614378396685708 - 5.6147104345463679643e-894j 7.13e-49, 2.14e-159j
0.012629753058388606247 + 2.1796294490614136257e-894j 5.07e-42, 1.52e-152j
0.032769165155848433568 + 2.0919013217973314578e-894j 1.61e-44, 4.84e-155j
0.039072614378396685708 - 1.1762590670498525954e-894j 2.15e-47, 6.45e-158j
0.012629753058388606247 - 5.2872403407058321015e-893j 1.06e-44, 3.18e-155j
0.037227889108837432398 + 7.3554982604592519131e-894j 6.92e-49, 2.08e-159j
0.035171528625758069638 - 1.0266771356449197639e-893j 3.61e-48, 1.09e-158j
0.049464325000999812949 + 9.902578445867645349e-895j 3.05e-54, 9.17e-165j
0.040740510243818817775 + 1.0777497391825654886e-894j 1.75e-50, 5.26e-161j
0.048665882198443086987 - 9.8328389410645122233e-895j 3.68e-54, 1.11e-164j
0.022714653977741888504 - 8.4661484449725876835e-893j 2.31e-47, 6.95e-158j
0.043541639766097430914 + 3.2204017994969181646e-894j 3.41e-53, 1.02e-163j
0.050730549818272237209 + 1.3819899452597144555e-894j 2.44e-56, 7.32e-167j
0.042224769943198387246 - 1.0205835982610377714e-894j 4.04e-52, 1.22e-162j
0.043541639766097430914 + 9.902687370900256993e-895j 4.23e-53, 1.27e-163j
0.051513247370403693117 - 1.1271341225392205761e-894j 2.03e-57, 6.1e-168j
0.042224769943198387246 - 3.7521176807304908129e-894j 5.18e-54, 1.56e-164j
0.040740510243818817775 + 4.5019936575087895109e-894j 1.99e-53, 5.98e-164j
0.05142115220552457993 + 1.0774778173163529891e-894j 3.14e-58, 9.45e-169j
0.044735163426795916527 - 9.7661675027184898055e-895j 5.44e-56, 1.64e-166j
0.050162221089434491685 - 1.0006410220538510438e-894j 5.96e-58, 1.79e-168j
0.048665882198443086987 - 1.8264496749706471734e-894j 2.24e-59, 6.72e-170j
0.045838005239078646024 + 2.5059997905461632076e-894j 7e-58, 2.1e-168j
0.05142115220552457993 + 1.1931839432359001883e-894j 2.55e-59, 7.66e-170j
0.047795250482917939924 + 9.7793690161862646872e-895j 1.14e-58, 3.42e-169j
0.045838005239078646024 + 9.7262892183992472109e-895j 3.2e-58, 9.64e-169j
0.051154360581145802656 - 1.2776191058898563471e-894j 6.26e-60, 1.88e-170j
0.046856555769645149622 - 2.2447143329994111579e-894j 4.67e-60, 1.4e-170j
0.049464325000999812949 + 1.6556421239760232488e-894j 8.41e-61, 2.53e-171j
0.050730549818272237209 + 1.0169239537637374728e-894j 7.74e-61, 2.33e-171j
0.046856555769645149622 - 9.7394585283523398603e-895j 2.58e-60, 7.76e-171j
0.051154360581145802656 - 1.0416614634988755878e-894j 5.05e-61, 1.52e-171j
0.050162221089434491685 - 1.5076638473868921963e-894j 1.03e-61, 3.1e-172j
0.047795250482917939924 + 2.0213491835511736432e-894j 1.01e-61, 3e-172j

Download

All rules of Legendre type can be downloaded here packed into a single file.