Rule: Q[1, 2, 6, 24, 36]

Type

This rule is of Hermite (physicists') 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)
8.4727814887129601515 - 9.9657534243813256119e-760j 9.76e-243, 9.76e-243j
-8.4727814887129601515 + 1.1604530780278024449e-762j 9.91e-243, 9.91e-243j
7.5447421564831677409 + 1.4016403188268741929e-759j 2.18e-241, 2.18e-241j
-7.9895252381268823201 - 1.925274525196123914e-761j 5.16e-242, 5.16e-242j
-9.0153819090839671607 + 4.326134514447657808e-763j 9.41e-244, 9.41e-244j
3.859641678951973708 - 4.1603912109406998527e-758j 2.33e-240, 2.33e-240j
-6.7335549105641932502 - 5.0312894411720253265e-760j 1.52e-240, 1.52e-240j
9.0153819090839671607 + 8.1879179493545157168e-763j 9.81e-244, 9.81e-244j
-1.6321716520540069475 + 2.1139944535777015837e-765j 1.58e-246, 1.58e-246j
3.3998220836348869732 + 4.3098320607763369529e-759j 9.2e-241, 9.2e-241j
9.6726006883249281038 + 7.7058248939832623101e-765j 4.63e-245, 4.63e-245j
4.1402732692721135161 - 8.8436960087525255046e-759j 7.27e-240, 7.27e-240j
-9.6726006883249281038 - 5.5233439983131858935e-774j 4.29e-245, 4.29e-245j
-4.1402732692721135161 + 3.9898859345470634835e-766j 7.21e-240, 7.21e-240j
-7.5447421564831677409 + 1.1893850203627588412e-767j 2.03e-241, 2.03e-241j
-2.9592107790638377223 + 2.7196814190366934382e-772j 5.34e-242, 5.34e-242j
1.6321716520540069475 + 7.3481317794296688896e-777j 1.59e-246, 1.59e-246j
-3.859641678951973708 + 6.0381573286692106511e-771j 2.26e-240, 2.26e-240j
-1.1969217051373895555 + 4.6435266375040035607e-777j 5.76e-247, 5.76e-247j
4.5607328812042278737 - 3.260514866124436048e-769j 1.53e-239, 1.53e-239j
5.1340784700752529115 - 2.6425405765396265527e-789j 1.85e-239, 1.85e-239j
1.1969217051373895555 - 1.200482629330927784e-809j 5.45e-247, 5.45e-247j
-5.3961532286066677345 - 1.1368845703325833604e-802j 1.79e-239, 1.79e-239j
6.7335549105641932502 - 1.1582757886628086611e-807j 1.61e-240, 1.61e-240j
-3.3998220836348869732 - 1.8563449640935007064e-814j 9.49e-241, 9.49e-241j
-4.5607328812042278737 - 2.7495171229483657434e-812j 1.46e-239, 1.46e-239j
3.227008194212813361 - 2.0504958831915974689e-813j 3.33e-241, 3.33e-241j
4.3406126076143357547 + 8.1715453548345073998e-812j 1.3e-239, 1.3e-239j
5.3961532286066677345 - 6.5388831962283187078e-818j 1.75e-239, 1.75e-239j
-1.2639774194296514651 + 5.1058694133857494235e-833j 8.72e-247, 8.72e-247j
-4.3406126076143357547 + 3.2977509643303852395e-824j 1.31e-239, 1.31e-239j
2.7526768121703306693 - 2.0940799673294578082e-828j 1.59e-242, 1.59e-242j
-6.0045998804986600715 + 2.6439503847276739304e-824j 6.78e-240, 6.78e-240j
7.9895252381268823201 + 3.4773021601384411534e-827j 5.09e-242, 5.09e-242j
7.1279922685877714596 - 1.6862792156578202684e-826j 7.31e-241, 7.31e-241j
-4.848988972613464028 + 4.7548037599110353481e-827j 1.48e-239, 1.48e-239j
1.2639774194296514651 - 3.8452665023239164498e-835j 8.43e-247, 8.43e-247j
2.5508337609312682057 + 1.2401430091253428967e-831j 2.94e-243, 2.94e-243j
2.0232301911005156592 + 4.097649671203375455e-834j 5.37e-245, 5.37e-245j
-2.7526768121703306693 - 4.1696495108415426988e-832j 1.61e-242, 1.61e-242j
-0.81784265210787922472 - 5.4625741616866434623e-839j 1.73e-250, 1.73e-250j
-6.3587880617000708972 - 7.2506423043191324831e-830j 3.4e-240, 3.4e-240j
6.3587880617000708972 + 1.8663700989329854597e-827j 3.36e-240, 3.36e-240j
4.848988972613464028 + 4.3248122378596277073e-837j 1.54e-239, 1.54e-239j
3.5703409224592463971 - 3.3407475614246242441e-849j 1.39e-240, 1.39e-240j
-1.8560194860375227093 + 7.2806121979611674702e-860j 1.61e-245, 1.61e-245j
-2.5508337609312682057 - 7.4945597646646524149e-858j 3.26e-243, 3.26e-243j
5.6788728765283782132 + 4.7743569726999184843e-853j 1.21e-239, 1.21e-239j
-7.1279922685877714596 + 7.2427168188090382873e-867j 6.28e-241, 6.28e-241j
0.81784265210787922472 - 4.2864043878108688661e-877j 1.79e-250, 1.79e-250j
-2.0232301911005156592 - 7.1618408097345867933e-871j 5.59e-245, 5.59e-245j
-1.2247448713915890491 - 1.2009868567683215709e-873j 1.19e-246, 1.19e-246j
-5.1340784700752529115 + 2.0227976345989471937e-865j 1.87e-239, 1.87e-239j
1.8560194860375227093 - 1.364575788806363679e-874j 1.62e-245, 1.62e-245j
1.2247448713915890491 + 2.3355852771237121436e-876j 1.33e-246, 1.33e-246j
6.0045998804986600715 - 3.960327349739703826e-869j 6.66e-240, 6.66e-240j
-0.52403354748695764515 - 2.6066672386050905394e-888j 9.69e-252, 9.69e-252j
-2.2833403693622945843 - 6.1809771629535738022e-880j 3.15e-244, 3.15e-244j
2.2833403693622945843 - 1.0867515891080908826e-880j 3.53e-244, 3.53e-244j
0.40103385448943630946 - 6.6625824546680422782e-890j 3.42e-252, 3.42e-252j
-3.5703409224592463971 + 2.2164190262591261206e-876j 1.44e-240, 1.44e-240j
-5.4876140580200934837e-915 + 1.5885365263806169878e-914j 1.16e-912, 1.16e-912j
-0.26999243649994017682 + 1.0244212714822954633e-890j 3.95e-253, 3.95e-253j
-5.6788728765283782132 - 5.5795575170019767528e-877j 1.11e-239, 1.11e-239j
0.52403354748695764515 + 4.2605965899684601952e-892j 8.94e-252, 8.94e-252j
2.9592107790638377223 - 4.9370139165863195227e-881j 5.6e-242, 5.6e-242j
-3.227008194212813361 - 4.5380505950034696786e-889j 3.56e-241, 3.56e-241j
-0.40103385448943630946 - 1.6085636419317974742e-901j 3.2e-252, 3.2e-252j
0.26999243649994017682 - 4.1802300508768950274e-903j 3.95e-253, 3.95e-253j

Weights

Weight (ball center) Error (ball radius)
1.9061324139671617121e-32 - 1.5606814943681312855e-784j 1.78e-75, 2.07e-194j
1.9061324139671617121e-32 + 5.8845074213751961055e-785j 7.05e-76, 8.21e-195j
4.6025548772605837033e-26 - 2.3178402985750763757e-780j 9.68e-73, 1.13e-191j
4.939593102628919345e-29 - 8.5568025388029732947e-783j 1.94e-74, 2.26e-193j
1.6607557514273223714e-36 - 1.8863039693046984894e-787j 4.38e-78, 5.1e-197j
5.632115879692254746e-08 + 1.5225189578062993037e-764j 2.37e-56, 2.76e-175j
4.4154142344520685336e-21 + 2.2171776433210394435e-777j 9.35e-71, 1.09e-189j
1.6607557514273223714e-36 + 4.6773312428873261339e-787j 3.41e-79, 3.97e-198j
0.010964217661312286856 + 2.039587903909276289e-761j 1.27e-35, 1.48e-154j
4.6974777445884996171e-07 + 1.9506346181898344226e-763j 4.28e-54, 4.98e-173j
1.000931630628592897e-41 - 3.3551334243332126357e-790j 8.59e-82, 1e-200j
5.1107620916433889075e-09 + 1.7666457264971289261e-765j 4.61e-59, 5.36e-178j
1.000931630628592897e-41 + 1.4503216981088282063e-790j 4.23e-82, 4.93e-201j
5.1107620916433889075e-09 - 4.8366473233122540381e-767j 8.25e-62, 9.6e-181j
4.6025548772605837033e-26 + 7.5651328788005696928e-781j 5.36e-75, 6.24e-194j
2.2304390028417701645e-05 + 8.4154721447179130191e-764j 1.19e-54, 1.39e-173j
0.010964217661312286856 + 5.046926343738634658e-761j 3.87e-42, 4.51e-161j
5.632115879692254746e-08 + 2.6697360940402337729e-766j 2.43e-60, 2.83e-179j
0.52909672579209490351 - 2.160837400198929593e-759j 6.3e-36, 7.34e-155j
1.4138568430437688648e-10 + 2.0364124989958130162e-767j 8.49e-65, 9.89e-184j
5.4689447504673650914e-13 + 8.338224155371115927e-770j 2.4e-68, 2.79e-187j
0.52909672579209490351 - 4.1140911583410175994e-759j 1.45e-38, 1.68e-157j
3.3472655083684985873e-14 + 1.1949231462567187708e-771j 6.45e-70, 7.51e-189j
4.4154142344520685336e-21 - 8.1577177255293042166e-777j 8.26e-76, 9.62e-195j
4.6974777445884996171e-07 + 1.2337251249139280669e-764j 9.24e-60, 1.08e-178j
1.4138568430437688648e-10 - 1.8253394961971834009e-768j 6.5e-66, 7.57e-185j
4.4715942367993662395e-06 - 2.8562544877878386237e-763j 2.07e-59, 2.41e-178j
6.3884163626182920593e-10 - 1.8654240318773388129e-766j 1.9e-64, 2.21e-183j
3.3472655083684985873e-14 - 7.0361878058146796784e-771j 1.35e-70, 1.58e-189j
0.32347207447314972679 - 1.3194277306335782232e-759j 2.43e-45, 2.83e-164j
6.3884163626182920593e-10 + 1.2944937639248801189e-767j 9.59e-66, 1.12e-184j
4.9588775415775893145e-05 - 1.4820383138673421274e-762j 3.39e-59, 3.95e-178j
4.2370082379865848602e-17 + 2.8945749107802882815e-774j 2.42e-74, 2.82e-193j
4.939593102628919345e-29 + 2.433061509848642319e-782j 1.98e-81, 2.31e-200j
1.9635248724396431878e-23 + 1.5600941327484230555e-778j 1.96e-78, 2.28e-197j
1.0195081318069279997e-11 + 1.3343660219699823105e-769j 6.45e-70, 7.5e-189j
0.32347207447314972679 - 2.6115850194865467047e-759j 9.03e-51, 1.05e-169j
0.00020725149783722767678 + 2.4450202551286984668e-762j 4.45e-60, 5.18e-179j
0.0020965059512597308459 + 1.7684643388753277184e-761j 1.01e-57, 1.18e-176j
4.9588775415775893145e-05 - 2.469618560277644287e-763j 7.38e-63, 8.6e-182j
0.086218422150295369721 + 1.280646315801670571e-760j 4.56e-52, 5.31e-171j
5.6677441044647718099e-19 - 8.7426468215854509444e-776j 8.25e-77, 9.6e-196j
5.6677441044647718099e-19 + 3.5362145528372866056e-775j 1.21e-76, 1.4e-195j
1.0195081318069279997e-11 - 1.1263693352454178038e-768j 4.85e-70, 5.64e-189j
4.4360061926939640284e-07 - 8.6774037913527719166e-764j 5.42e-65, 6.31e-184j
0.00281765445659690582 - 1.1801104663562558944e-761j 1.88e-61, 2.19e-180j
0.00020725149783722767678 + 4.9653300893598618969e-763j 1.13e-64, 1.32e-183j
1.7040375501771809383e-15 + 3.8950518339778330264e-772j 1.82e-74, 2.12e-193j
1.9635248724396431878e-23 - 4.699822642293124672e-779j 9.65e-82, 1.12e-200j
0.086218422150295369721 + 1.972695930199164879e-760j 5.91e-60, 6.88e-179j
0.0020965059512597308459 + 5.4950493060996424044e-762j 2.23e-63, 2.59e-182j
-0.78599085808809739347 + 3.4177040490086657063e-759j 1.39e-58, 1.62e-177j
5.4689447504673650914e-13 - 1.2165570972361040891e-770j 3.01e-74, 3.51e-193j
0.00281765445659690582 - 3.3806584196993013029e-761j 3.32e-63, 3.86e-182j
-0.78599085808809739347 + 6.6124065654996637347e-759j 6.43e-60, 7.48e-179j
4.2370082379865848602e-17 - 1.3119375129999639475e-773j 1.12e-76, 1.31e-195j
0.12998886822613144794 - 5.0896374086266266072e-760j 4.15e-62, 4.83e-181j
0.00084779539011754839088 - 1.2839698274444675378e-762j 2.01e-65, 2.34e-184j
0.00084779539011754839088 - 5.0296601187149050373e-762j 3.43e-65, 3.98e-184j
-0.025221562228827634674 + 1.1463923017007652836e-759j 2e-63, 2.32e-182j
4.4360061926939640284e-07 - 3.0277185101735437483e-765j 1.33e-69, 1.55e-188j
0.14917133942066959929 + 3.8176875840382641384e-760j 5e-64, 5.8e-183j
0.15083989467679495517 - 6.846726221214457415e-760j 5.89e-64, 6.84e-183j
1.7040375501771809383e-15 - 7.5656188195218434515e-773j 2.41e-77, 2.81e-196j
0.12998886822613144794 - 6.696135106854757814e-760j 3.64e-64, 4.21e-183j
2.2304390028417701645e-05 + 6.3814716898270148111e-763j 3.25e-68, 3.8e-187j
4.4715942367993662395e-06 - 2.6204406887708693299e-764j 7.66e-69, 8.94e-188j
-0.025221562228827634674 + 9.2981103102874438821e-760j 2.2e-64, 2.62e-183j
0.15083989467679495517 - 7.8810694281879447362e-760j 1.41e-64, 1.58e-183j

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.