Rule: Q[2, 4, 29, 36]

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)
-0.99760970543424740224 - 2.1983505918103791008e-870j 5.4e-230, 5.4e-230j
-0.96959513022871262378 - 2.6356257812118557753e-872j 6.02e-230, 6.02e-230j
-0.9292713465849212511 - 8.9346184544413037775e-873j 1.35e-230, 1.35e-230j
-0.99357534717728902447 - 1.9345808303979006867e-871j 8.32e-230, 8.32e-230j
0.94443029831945333252 - 3.1570850111939135771e-873j 2.4e-230, 2.4e-230j
0.9292713465849212511 + 7.1473942401526492751e-874j 1.28e-230, 1.28e-230j
0.95790268279466651143 + 7.242604752366358007e-875j 4.08e-230, 4.08e-230j
-0.91248695683407599658 - 1.7136923502684805333e-894j 6.72e-231, 6.72e-231j
0.99357534717728902447 + 7.3813357339623421909e-892j 7.71e-230, 7.71e-230j
0.99960131825172612385 + 1.5900961646143164114e-918j 2.09e-230, 2.09e-230j
0.87393509723304819617 + 2.0234102286902450137e-943j 8.71e-232, 8.71e-232j
0.97946416088735537194 + 4.4690009901306674711e-942j 7.51e-230, 7.51e-230j
-0.94443029831945333252 - 8.2656001098478457788e-956j 2.34e-230, 2.34e-230j
-0.82852300212779487549 + 6.4896152481557282397e-958j 7.43e-233, 7.43e-233j
0.99760970543424740224 - 3.1112385903934228872e-952j 5.3e-230, 5.3e-230j
0.91248695683407599658 - 1.2066204005259394269e-965j 6.21e-231, 6.21e-231j
0.89405568945089307213 - 3.0874136790119114014e-966j 2.66e-231, 2.66e-231j
-0.99960131825172612385 - 1.5263993265258211325e-965j 2.19e-230, 2.19e-230j
-0.80314462337259800082 + 3.3053443448954666965e-971j 1.92e-233, 1.92e-233j
-0.89405568945089307213 + 7.8860708989634587162e-969j 2.41e-231, 2.41e-231j
0.85210306922271128894 - 5.9771976529543992876e-968j 2.7e-232, 2.7e-232j
0.77595250415319466515 + 5.9575254352039258511e-971j 3.66e-234, 3.66e-234j
-0.87393509723304819617 - 4.7384469682196319046e-969j 8.91e-232, 8.91e-232j
-0.7469757890578960909 + 1.7346306082418815156e-972j 6.99e-235, 6.99e-235j
-0.77595250415319466515 + 3.4869127565120364338e-972j 3.59e-234, 3.59e-234j
0.98748610447248284002 - 1.1323367181919327512e-964j 7.73e-230, 7.73e-230j
0.80314462337259800082 - 6.5735960486168088205e-979j 1.83e-233, 1.83e-233j
0.82852300212779487549 - 4.3058482139297871487e-978j 7.9e-233, 7.9e-233j
0.96959513022871262378 + 1.2105467211275229936e-975j 6.3e-230, 6.3e-230j
-0.6498489178674061656 - 1.8217361631728653221e-984j 2.13e-237, 2.13e-237j
0.20007931941034711386 + 9.7359870590291451491e-997j 8.96e-250, 8.96e-250j
0.15655801081562154215 - 3.2279225127995906287e-998j 5.15e-251, 5.15e-251j
0.68386130861924166871 + 1.6014649153257347215e-985j 1.65e-236, 1.65e-236j
-0.98748610447248284002 + 1.0534724616422221941e-975j 8.38e-230, 8.38e-230j
-0.68386130861924166871 + 1.7937919406432370296e-985j 1.7e-236, 1.7e-236j
-0.71626077567689709711 + 7.1353480041807921901e-985j 1.13e-235, 1.13e-235j
0.7469757890578960909 - 1.1152844956914767373e-984j 6.86e-235, 6.86e-235j
0.57735026918962576451 - 4.5584102320193497569e-990j 2.51e-239, 2.51e-239j
0.61431326488613617062 + 3.4213700631317916614e-988j 2.72e-238, 2.72e-238j
-0.85210306922271128894 + 5.4770681518911343445e-981j 2.82e-232, 2.82e-232j
-0.53905677061753625793 - 1.0728710841398232421e-989j 2.33e-240, 2.33e-240j
-0.97946416088735537194 + 1.3746440087449645628e-977j 7.12e-230, 7.12e-230j
0.6498489178674061656 - 7.3306798246207455951e-989j 2.17e-237, 2.17e-237j
0.53905677061753625793 + 2.1887096729329652834e-992j 2.29e-240, 2.29e-240j
-3.074681522774186527e-1035 - 2.0450993403887818055e-1035j 2.62e-1033, 2.62e-1033j
-0.57735026918962576451 + 5.4276606639492277685e-990j 2.65e-239, 2.65e-239j
-0.61431326488613617062 - 1.2805257338271555172e-988j 2.6e-238, 2.6e-238j
-0.20007931941034711386 - 1.2895035824643046815e-1000j 9.27e-250, 9.27e-250j
0.49953703163638994193 - 9.2546627696100031393e-993j 1.95e-241, 1.95e-241j
0.71626077567689709711 - 1.9043267980856096723e-987j 1.25e-235, 1.25e-235j
-0.41729651639906670022 + 1.3990500511938755876e-994j 1.1e-243, 1.1e-243j
-0.45890813061046436553 - 2.7625864060196724878e-994j 1.53e-242, 1.53e-242j
-0.95790268279466651143 + 4.7373947462689442181e-1000j 3.84e-230, 3.84e-230j
0.45890813061046436553 + 1.0161851429210675047e-1015j 1.63e-242, 1.63e-242j
0.41729651639906670022 + 5.2837907299636102408e-1019j 1.32e-243, 1.32e-243j
-0.073618824281943662477 + 3.0478813673340798829e-1026j 2.16e-253, 2.16e-253j
-0.49953703163638994193 + 7.6094860361980756059e-1015j 1.94e-241, 1.94e-241j
-0.28799377397515002378 - 4.8826554150760768886e-1020j 2.7e-247, 2.7e-247j
0.035798254255691507226 - 2.834196664905247915e-1028j 1.35e-254, 1.35e-254j
0.37483518598739759301 + 7.3352951631343204681e-1018j 8.79e-245, 8.79e-245j
0.073618824281943662477 - 2.8731636712333467877e-1026j 2.16e-253, 2.16e-253j
-0.24402958546140932086 + 1.0742427940862652171e-1021j 1.61e-248, 1.61e-248j
-0.37483518598739759301 - 7.0976431643664342269e-1018j 7.99e-245, 7.99e-245j
-0.035798254255691507226 - 2.6295060550658207751e-1027j 1.35e-254, 1.35e-254j
0.28799377397515002378 + 2.1371897041080314849e-1020j 2.69e-247, 2.69e-247j
0.24402958546140932086 - 1.5368257277509486266e-1021j 1.5e-248, 1.5e-248j
-0.15655801081562154215 + 9.0594570647196834309e-1024j 5.36e-251, 5.36e-251j
-0.33167317545643584886 + 9.1254564161147256829e-1019j 5.16e-246, 5.16e-246j
-0.1141029159441040519 - 5.3111998685975476053e-1025j 3.03e-252, 3.03e-252j
0.1141029159441040519 + 6.8236436581498808314e-1025j 3.15e-252, 3.15e-252j
0.33167317545643584886 - 8.1392973700067160922e-1019j 5.15e-246, 5.15e-246j

Weights

Weight (ball center) Error (ball radius)
0.0029854242706421527299 - 8.4597599752747174188e-871j 1.11e-18, 1.4e-126j
0.010783143745234586787 - 9.0675514490264467316e-871j 4.16e-19, 5.22e-127j
0.015974427062143679088 + 6.7786852661307063524e-871j 2.13e-19, 2.68e-127j
0.0050791966591110238481 + 2.6789629779327726454e-870j 4.44e-19, 5.57e-127j
0.014332142803989794939 - 2.0351391642316633068e-872j 1.83e-20, 2.3e-128j
0.015974427062143679088 + 2.032685838653309582e-872j 1.04e-20, 1.31e-128j
0.012595205151110361236 + 1.9558400320860171477e-872j 7.49e-21, 9.39e-129j
0.017599471732452930944 - 6.0954302418179977342e-871j 2.56e-21, 3.21e-129j
0.0050791966591110238481 + 5.3499014548771409838e-873j 2.19e-22, 2.74e-130j
0.0010717501795698874837 + 1.0623988521658709441e-873j 5.58e-23, 7e-131j
0.020972816748724860965 - 3.110310199447820276e-872j 2.31e-24, 2.9e-132j
0.0089528856750941926696 + 1.0851181537723548377e-872j 2.29e-23, 2.88e-131j
0.014332142803989794939 - 7.5023292467137602222e-871j 4.12e-25, 5.16e-133j
0.024472305684981059152 - 3.6368681578482862556e-871j 7.04e-27, 8.83e-135j
0.0029854242706421527299 - 3.1755883180655308996e-873j 7.56e-23, 9.48e-131j
0.017599471732452930944 - 2.4787620534140970621e-872j 4.22e-24, 5.29e-132j
0.019271012898552680118 + 2.8626055820941196034e-872j 1.18e-24, 1.47e-132j
0.0010717501795698874837 - 1.0734266086342164722e-870j 1.7e-26, 2.13e-134j
0.026287138248840046337 + 3.0864504657254655488e-871j 1.36e-28, 1.71e-136j
0.019271012898552680118 + 5.5160605416757757078e-871j 2.34e-27, 2.93e-135j
0.022697347086031091571 + 3.2501054773085217999e-872j 9.59e-28, 1.2e-135j
0.028091594711094031698 - 3.2235406220567272512e-872j 3.84e-30, 4.81e-138j
0.020972816748724860965 - 4.8823985657670877703e-871j 5.02e-28, 6.3e-136j
0.029853976768050371796 + 2.2278147084973220082e-871j 6.2e-31, 7.78e-139j
0.028091594711094031698 - 2.6151209257940434798e-871j 4.09e-30, 5.13e-138j
0.0070762504021480740692 - 7.8339069334189417451e-873j 7.57e-27, 9.5e-135j
0.026287138248840046337 + 3.2773254053139651225e-872j 1.47e-30, 1.84e-138j
0.024472305684981059152 - 3.297243324796608986e-872j 7.65e-30, 9.6e-138j
0.010783143745234586787 - 1.4551425418325727716e-872j 3.37e-27, 4.22e-135j
0.034789903822686552879 - 1.4902931929636558283e-871j 7.17e-36, 9e-144j
0.043819201270646318715 + 1.6830376477173108839e-871j 1.25e-38, 1.57e-146j
0.043119092765144808746 - 2.4534188267418604609e-871j 9.59e-39, 1.2e-146j
0.033219671769449199238 + 3.1005485366672808592e-872j 9.17e-36, 1.15e-143j
0.0070762504021480740692 - 1.3316806122412333378e-870j 1.86e-33, 2.34e-141j
0.033219671769449199238 + 1.6753820027236532602e-871j 2.15e-36, 2.7e-144j
0.031567347106719802766 - 1.9179156983534432328e-871j 9.84e-36, 1.23e-143j
0.029853976768050371796 + 3.164042990543030294e-872j 3.69e-35, 4.63e-143j
0.037644691099143924937 - 3.3374867817464229779e-872j 2.53e-39, 3.17e-147j
0.036265312865713697713 + 3.1990122411127431985e-872j 1.06e-38, 1.33e-146j
0.022697347086031091571 + 4.2453253054893798769e-871j 5.17e-36, 6.49e-144j
0.038925043328897415061 + 1.1965265323959706878e-871j 5.59e-42, 7.01e-150j
0.0089528856750941926696 + 1.0372414746755351991e-870j 4.36e-36, 5.46e-144j
0.034789903822686552879 - 3.1237981708977299638e-872j 7.79e-39, 9.76e-147j
0.038925043328897415061 + 3.5543791881517005626e-872j 4.72e-41, 5.92e-149j
0.03540896480858666132 - 9.0042487512622549011e-871j 1.74e-45, 2.18e-153j
0.037644691099143924937 - 1.2573164149600273403e-871j 3.81e-42, 4.78e-150j
0.036265312865713697713 + 1.3534915696234238198e-871j 2.09e-41, 2.62e-149j
0.043819201270646318715 + 2.5304827211993880658e-871j 3.9e-47, 4.88e-155j
0.040094833209316417596 - 3.872479624681215934e-872j 1.09e-43, 1.37e-151j
0.031567347106719802766 - 3.1181726796923386371e-872j 3.31e-40, 4.16e-148j
0.04205942275902673999 - 1.2143518816676047073e-871j 2.81e-46, 3.53e-154j
0.041141809614003225999 + 1.1735840245082215351e-871j 1.17e-45, 1.46e-153j
0.012595205151110361236 + 8.3215235478241782037e-871j 1.18e-40, 1.48e-148j
0.041141809614003225999 + 4.3258454595341145236e-872j 1.17e-45, 1.46e-153j
0.04205942275902673999 - 4.9660010509876598128e-872j 1.23e-46, 1.54e-154j
0.039193827248394512301 - 6.5216020978399501428e-871j 1.26e-49, 1.58e-157j
0.040094833209316417596 - 1.1686009511003850481e-871j 2.44e-46, 3.06e-154j
0.043865253010510302592 + 1.6579149664139731954e-871j 1.63e-49, 2.04e-157j
0.036552149279309634159 + 7.7890134501188273046e-871j 6.33e-50, 7.94e-158j
0.042838743568225539628 + 5.8747551722518024724e-872j 1.57e-49, 1.98e-157j
0.039193827248394512301 - 5.6228780993970423486e-871j 2.94e-50, 3.68e-158j
0.044014080392667193194 - 1.9989043074248035586e-871j 1.17e-50, 1.47e-158j
0.042838743568225539628 + 1.297910987823035837e-871j 3.25e-50, 4.07e-158j
0.036552149279309634159 + 8.3705115698098356998e-871j 1.19e-50, 1.5e-158j
0.043865253010510302592 + 9.1348376126332919682e-872j 5.02e-52, 6.3e-160j
0.044014080392667193194 - 1.2113949796477879729e-871j 6.74e-52, 8.45e-160j
0.043119092765144808746 - 3.3698598027720322695e-871j 2.79e-52, 3.5e-160j
0.043454974742847010442 - 1.4378123785905280058e-871j 2.47e-52, 3.1e-160j
0.041634069915233547951 + 4.6807338701906051832e-871j 2.76e-52, 3.46e-160j
0.041634069915233547951 + 3.7174747063730059889e-871j 9.25e-53, 1.17e-160j
0.043454974742847010442 - 7.187708547942689667e-872j 1.87e-53, 2.29e-161j

Download

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