Rule: Q[2, 14, 17, 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.

Warning: This rule has negative weights!

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)
0.99942571559104619649 + 1.0167207169202149765e-868j 4.93e-232, 4.93e-232j
-0.97925804742115315144 + 1.1018715797735029223e-866j 4.57e-232, 4.57e-232j
-0.93798437900993878791 - 1.3441258395227813008e-877j 6.65e-233, 6.65e-233j
-0.98812513120329170302 - 1.4906200335480799176e-890j 7.02e-232, 7.02e-232j
0.93798437900993878791 - 5.1220149113439861135e-919j 6.35e-233, 6.35e-233j
0.95438178131849995168 + 5.7950490908114897029e-919j 1.44e-232, 1.44e-232j
-0.99942571559104619649 + 4.9260418033976600491e-914j 5.13e-232, 5.13e-232j
-0.87540955680565990435 + 6.3929210739180227707e-942j 3.67e-234, 3.67e-234j
-0.27284897762140606314 + 1.4499881974365303332e-968j 4.04e-248, 4.04e-248j
-0.99801892256191654731 - 8.2145477566631695456e-950j 1.04e-231, 1.04e-231j
0.87540955680565990435 + 6.8012157970126935083e-970j 3.76e-234, 3.76e-234j
0.97925804742115315144 - 6.3409964953304235217e-966j 4.51e-232, 4.51e-232j
-0.91924740176136484784 - 1.2240238794271177041e-967j 2.88e-233, 2.88e-233j
-0.85001680456214491633 + 2.9678585152245363937e-970j 1.09e-234, 1.09e-234j
0.98812513120329170302 + 8.788267605613283855e-967j 6.56e-232, 6.56e-232j
0.85001680456214491633 + 5.4768251845223443518e-971j 1.15e-234, 1.15e-234j
0.91924740176136484784 - 1.1157565981390422038e-968j 2.7e-233, 2.7e-233j
-0.99457933162336099035 - 6.4320088554253823671e-966j 9e-232, 9e-232j
-0.761605801755859564 - 1.2609141169445841602e-976j 1.4e-236, 1.4e-236j
-0.96811291912570600223 + 4.6807190796603189272e-971j 2.53e-232, 2.53e-232j
0.89843346559934327684 - 3.0115316479996282242e-976j 1.16e-233, 1.16e-233j
0.761605801755859564 - 1.8392974372797337312e-979j 1.45e-236, 1.45e-236j
-0.95438178131849995168 - 4.6588460312002218687e-976j 1.38e-232, 1.38e-232j
-0.82247396120800798233 - 7.1985713294490669911e-979j 3.02e-235, 3.02e-235j
-0.79304471295578093547 - 7.9098713950801618075e-981j 6.98e-236, 6.98e-236j
0.96811291912570600223 - 4.7132030154083472466e-974j 2.63e-232, 2.63e-232j
0.72799373091578229991 - 1.2131797629415934162e-979j 2.66e-237, 2.66e-237j
0.82247396120800798233 - 5.90177042509036979e-978j 2.92e-235, 2.92e-235j
0.99457933162336099035 - 5.2609930364530731469e-973j 9.24e-232, 9.24e-232j
-0.65575301930606699162 + 1.960235664659365678e-986j 7.12e-239, 7.12e-239j
0.99801892256191654731 - 6.1866249441150908167e-984j 1.1e-231, 1.1e-231j
0.79304471295578093547 + 1.8611629819809742697e-986j 7.15e-236, 7.15e-236j
0.6925444693880536229 - 8.7704849767571290277e-989j 4.38e-238, 4.38e-238j
0.61749826287397070064 + 1.6800687312790801296e-990j 1.02e-239, 1.02e-239j
-0.61749826287397070064 + 2.041892128168346895e-990j 9.27e-240, 9.27e-240j
-0.72799373091578229991 - 1.0531870249335141647e-986j 2.68e-237, 2.68e-237j
0.65575301930606699162 - 5.0269249356525978638e-990j 7.03e-239, 7.03e-239j
0.57735026918962576451 - 2.8793475222667857019e-992j 1.14e-240, 1.14e-240j
0.27284897762140606314 + 3.6324670323135780716e-999j 4.03e-248, 4.03e-248j
-0.6925444693880536229 + 1.1029908885411634301e-987j 4.55e-238, 4.55e-238j
-0.57735026918962576451 + 9.5353868990795621996e-991j 1.04e-240, 1.04e-240j
-0.89843346559934327684 - 4.5357500797801512292e-999j 1.07e-233, 1.07e-233j
0.45069079930973050852 + 1.2393087761586468816e-1009j 1.04e-243, 1.04e-243j
0.53572802714228451342 + 7.0274140709949774811e-1008j 1.16e-241, 1.16e-241j
-5.1992556398128808772e-1057 + 3.5751953141592058838e-1057j 4.1e-1055, 4.1e-1055j
-0.49362076485802038841 + 2.0306602272844845673e-1007j 1.26e-242, 1.26e-242j
-0.53572802714228451342 - 1.0187377208249433603e-1009j 1.16e-241, 1.16e-241j
0.15169853642916601023 + 1.3848374834728358917e-1018j 6.01e-250, 6.01e-250j
0.49362076485802038841 - 8.174432603718643191e-1012j 1.24e-242, 1.24e-242j
0.14557234721025513197 + 3.2667451581197647184e-1019j 6.79e-250, 6.79e-250j
-0.31450259120229373939 + 5.6615420298546456085e-1016j 4.97e-247, 4.97e-247j
-0.45069079930973050852 - 4.3809868154241932524e-1012j 1.01e-243, 1.01e-243j
-0.13746449867876437507 - 3.447484603263953722e-1019j 1.84e-250, 1.84e-250j
0.22374161346734564129 - 9.2632334428997539859e-1019j 1.88e-249, 1.88e-249j
0.35866289349246012419 + 2.1779462291883551141e-1016j 5.88e-246, 5.88e-246j
-0.14557234721025513197 - 2.8776736471328653798e-1019j 6.97e-250, 6.97e-250j
-0.40545074306610185911 + 4.4847637798241666556e-1013j 8.18e-245, 8.18e-245j
-0.15169853642916601023 + 1.4654614593651600965e-1018j 6.29e-250, 6.29e-250j
0.061237645707923134607 + 5.662471107054305742e-1023j 4.53e-254, 4.53e-254j
0.40545074306610185911 - 3.2758837319353717057e-1014j 8.2e-245, 8.2e-245j
0.13746449867876437507 - 1.1653356696625370518e-1019j 1.86e-250, 1.86e-250j
-0.22374161346734564129 + 6.6343481629594702621e-1019j 1.87e-249, 1.87e-249j
-0.35866289349246012419 - 8.3641975837792477418e-1015j 6.07e-246, 6.07e-246j
-0.061237645707923134607 - 7.1089579093263827071e-1023j 4.84e-254, 4.84e-254j
0.31450259120229373939 + 3.4415946474728242188e-1016j 5.21e-247, 5.21e-247j

Weights

Weight (ball center) Error (ball radius)
0.0012566503195062431791 - 1.3189264762366460573e-868j 8.99e-29, 1.31e-137j
0.0099755978014114919873 - 8.9927457711967731592e-868j 4.44e-29, 6.49e-138j
0.017635643304911319899 - 2.7596576793713632195e-867j 1.53e-29, 2.24e-138j
0.0077333752927005168932 + 1.2097485524755152228e-866j 2.51e-29, 3.68e-138j
0.017635643304911319899 - 5.4708547768355928352e-869j 4.52e-31, 6.61e-140j
0.015094996824517627314 + 5.1397646341089672288e-869j 4.42e-31, 6.46e-140j
0.0012566503195062431791 - 2.4971170970159814978e-867j 1.66e-30, 2.42e-139j
0.024212013878996586789 + 1.2979667116022723414e-867j 1.42e-32, 2.07e-141j
0.044097435553808038904 + 1.5816817148860426868e-867j 1.58e-34, 2.31e-143j
0.0018827531810331451608 + 5.9646224946538882421e-867j 1.91e-30, 2.79e-139j
0.024212013878996586789 + 6.9929422054283577027e-869j 3.16e-34, 4.62e-143j
0.0099755978014114919873 + 4.2295642362288287735e-869j 5.75e-34, 8.4e-143j
0.019786760099179592016 + 2.0055777919503242887e-867j 1.45e-32, 2.12e-141j
0.026529263618607960115 - 1.1001583227070803451e-867j 1.03e-33, 1.51e-142j
0.0077333752927005168932 - 3.0440724750720950933e-869j 1.92e-34, 2.8e-143j
0.026529263618607960115 - 7.532691146164505181e-869j 1.1e-35, 1.6e-144j
0.019786760099179592016 + 5.9591459877738901566e-869j 8.83e-35, 1.29e-143j
0.0050658954149663059383 - 7.4952635752366675859e-867j 4.87e-31, 7.12e-140j
0.032533301850279181155 + 8.0451856018161220723e-868j 2.93e-36, 4.28e-145j
0.012382850502513463241 - 1.0024129534075939361e-866j 2.11e-32, 3.08e-141j
0.021871770101574467813 - 6.4984477497175412991e-869j 5.64e-36, 8.25e-145j
0.032533301850279181155 + 9.8748211252507925989e-869j 2.47e-39, 3.61e-148j
0.015094996824517627314 + 4.483307519827045129e-867j 8.6e-33, 1.26e-141j
0.02850217223797135361 + 9.7046502217233531878e-868j 5.52e-36, 8.07e-145j
0.030384567250162965984 - 8.7814118383471586778e-868j 1.18e-36, 1.72e-145j
0.012382850502513463241 - 4.8318498874079219957e-869j 1.57e-36, 2.29e-145j
0.034627758868595315594 - 1.0935188074563561172e-868j 1.67e-40, 2.45e-149j
0.02850217223797135361 + 8.2284890862916023236e-869j 6.79e-39, 9.93e-148j
0.0050658954149663059383 - 1.9373097429560752579e-870j 1.4e-37, 2.05e-146j
0.03743721370667741162 - 7.3180076240500586901e-868j 5.57e-44, 8.14e-153j
0.0018827531810331451608 + 1.4521083097096359786e-868j 1.48e-37, 2.17e-146j
0.030384567250162965984 - 9.0278647431550515832e-869j 9.29e-41, 1.36e-149j
0.036170504466727683756 + 1.2433531253816094678e-868j 1.38e-43, 2.01e-152j
0.039171989886524404653 + 1.638939655159031463e-868j 1e-45, 1.47e-154j
0.039171989886524404653 + 7.3074503655156452497e-868j 3.91e-47, 5.71e-156j
0.034627758868595315594 - 7.5477747389930456567e-868j 2.29e-45, 3.34e-154j
0.03743721370667741162 - 1.4311816676998463006e-868j 3.31e-45, 4.85e-154j
0.041049793490876584687 - 1.8975723275225562932e-868j 2.63e-47, 3.85e-156j
0.044097435553808038904 + 8.8969912335311211522e-868j 1.23e-51, 1.8e-160j
0.036170504466727683756 + 7.3483327047379407396e-868j 1.54e-46, 2.26e-155j
0.041049793490876584687 - 7.4140074676731231128e-868j 6.46e-49, 9.45e-158j
0.021871770101574467813 - 1.5842663787542891102e-867j 6.83e-45, 9.99e-154j
0.043917501955254953652 + 3.2792176227565274487e-868j 9.93e-51, 1.45e-159j
0.041988845641254987669 + 2.2759149758536780153e-868j 3.57e-49, 5.22e-158j
0.060950190054690083795 + 5.7672706462685159993e-868j 6.22e-54, 9.1e-163j
0.042273836045791638334 - 8.4363368703261522633e-868j 1.62e-51, 2.37e-160j
0.041988845641254987669 + 7.8331799652116799788e-868j 1.35e-50, 1.97e-159j
0.66224525825169128498 + 3.5303175584336639186e-866j 2.36e-54, 3.44e-163j
0.042273836045791638334 - 2.763357375653509306e-868j 4.26e-52, 6.23e-161j
-1.074841871241706199 - 6.0310001626973597623e-866j 2.15e-54, 3.14e-163j
0.041601968308554507405 - 1.4802896686265637244e-867j 9.95e-56, 1.46e-164j
0.043917501955254953652 + 8.922149499294801228e-868j 1.6e-54, 2.34e-163j
0.51594196969432975555 + 3.4572912801904521419e-866j 3.19e-57, 4.66e-166j
0.054206081617696676338 - 1.0296274074055800991e-867j 7.84e-57, 1.15e-165j
0.046355936971854536772 + 5.4072803377169203443e-868j 7.8e-57, 1.14e-165j
-1.074841871241706199 - 8.149387587111208982e-866j 1.89e-57, 2.77e-166j
0.046451974183296906324 - 9.6477372196078955864e-868j 2.93e-58, 4.29e-167j
0.66224525825169128498 + 4.8321463638773223448e-866j 1.05e-57, 1.54e-166j
0.061981095893094249783 - 7.1973907718219511321e-868j 1.06e-59, 1.54e-168j
0.046451974183296906324 - 3.9783873542226338038e-868j 2.25e-59, 3.28e-168j
0.51594196969432975555 + 2.6024538633405198615e-866j 3.38e-58, 4.95e-167j
0.054206081617696676338 - 1.6433602282412085091e-867j 4.17e-60, 6.1e-169j
0.046355936971854536772 + 1.1705876307524093045e-867j 3.14e-60, 4.58e-169j
0.061981095893094249783 - 8.1626663251485078603e-868j 1.45e-60, 2.14e-169j
0.041601968308554507405 - 7.5792497542273405536e-868j 1.48e-60, 2.05e-169j

Download

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