Rule: Q[4, 9, 94]

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.

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)
11.241672484718744893 - 1.2208106202482902361e-2069j 3.22e-999, 3.22e-999j
10.237161907544437147 - 2.8524818958181099872e-2067j 1.29e-997, 1.29e-997j
4.0613239531173431814 - 1.8351763989742409521e-2071j 1.18e-1001, 1.18e-1001j
12.00200298657122261 + 5.3688673605826155542e-2071j 7.92e-1001, 7.92e-1001j
1.6506801238857845559 + 1.2689540724863285346e-2081j 8.1e-1011, 8.1e-1011j
10.892661428160584298 + 1.23787804026219028e-2068j 1.26e-998, 1.26e-998j
12.428675433919729811 + 1.5688054082988984729e-2071j 7.83e-1002, 7.83e-1002j
2.4994001356249370327 - 1.1200986896604384194e-2076j 9.46e-1007, 9.46e-1007j
1.8579289724946339736 - 1.8469685464270375056e-2079j 8.19e-1010, 8.19e-1010j
12.908187500966365139 + 1.6086318632385949865e-2073j 4.01e-1003, 4.01e-1003j
1.4490965895233053378 - 2.7604043820081883803e-2081j 8.17e-1012, 8.17e-1012j
8.213166061109724224 - 1.2121719315241093541e-2066j 2.87e-996, 2.87e-996j
6.6664670104660117931 + 3.2773797398794554928e-2067j 5.42e-997, 5.42e-997j
2.9263645536597399004 + 1.5536015970666214165e-2074j 2.96e-1004, 2.96e-1004j
10.558711754748694577 - 3.67888125853422586e-2068j 4.51e-998, 4.51e-998j
5.4541126887358558191 + 1.9314667711318539154e-2068j 1.09e-998, 1.09e-998j
9.0419425189672695474 + 2.8466543329916063839e-2067j 1.64e-996, 1.64e-996j
11.609534773773414555 + 2.6497170784234195529e-2070j 6e-1000, 6e-1000j
6.1747663347029431356 + 1.7398012921392416354e-2067j 1.48e-997, 1.48e-997j
8.4843660807688419175 + 2.1356181498936708483e-2066j 2.77e-996, 2.77e-996j
9.6238901239691935554 - 6.5772063491401622003e-2067j 6.1e-997, 6.1e-997j
9.926052880765454393 - 4.1507431512027204744e-2067j 3.34e-997, 3.34e-997j
5.2178340171465813101 - 2.0748456859805483899e-2070j 3.97e-999, 3.97e-999j
9.3295006620009277994 - 1.9932406696351595191e-2066j 1.07e-996, 1.07e-996j
1.2551527310423468231 - 1.5284199921992776236e-2082j 8.41e-1013, 8.41e-1013j
7.1688186558445482346 + 5.199919628194097061e-2066j 1.38e-996, 1.38e-996j
3.609213199836183544 - 1.0465403354606697708e-2072j 7.54e-1003, 7.54e-1003j
4.5192710191831587742 + 2.6629032341874752478e-2070j 1.52e-1000, 1.52e-1000j
3.3855432781284968142 + 2.1969057928527980847e-2074j 2.09e-1003, 2.09e-1003j
8.7604447186513183834 - 3.1450971324200031369e-2066j 2.24e-996, 2.24e-996j
3.8345325314433831864 + 2.065804172804677283e-2072j 3e-1002, 3e-1002j
6.419382591282156486 - 3.8503753270073320168e-2067j 2.91e-997, 2.91e-997j
2.0691626986869960821 + 1.4812132762767498717e-2078j 8.82e-1009, 8.82e-1009j
4.7505039662432625641 + 4.0617602462790540824e-2070j 4.7e-1000, 4.7e-1000j
5.9324484985156980773 + 7.8129935079554133604e-2068j 6.48e-998, 6.48e-998j
13.489347255723870127 - 6.2823822245979314773e-2075j 7.83e-1005, 7.83e-1005j
7.9463835836425496153 - 2.0281683684132955843e-2066j 2.95e-996, 2.95e-996j
4.2895616337236207733 + 4.2018177846116305929e-2071j 4.1e-1001, 4.1e-1001j
4.9833302245568576804 - 3.4737107068525229277e-2069j 1.38e-999, 1.38e-999j
3.1646264004517797537 + 6.3088026828261317948e-2074j 7.72e-1004, 7.72e-1004j
2.2832506552235534748 - 6.4811353648911337881e-2078j 8.31e-1008, 8.31e-1008j
2.9899278943630500681 - 2.5545762216707347002e-2074j 5.48e-1004, 5.48e-1004j
2.7166709002873981457 + 4.2342554261107830299e-2077j 1.16e-1005, 1.16e-1005j
7.6836213369996262221 + 2.0205939255398879175e-2066j 2.39e-996, 2.39e-996j
7.4245339057704326501 - 5.1331330407225035928e-2066j 1.87e-996, 1.87e-996j
6.91620863943432204 + 7.2268944928189675521e-2067j 8.81e-997, 8.81e-997j
5.6922764034722333794 - 5.1907234351813222343e-2068j 2.74e-998, 2.74e-998j
-10.892661428160584298 - 6.0346108140484705307e-2065j 1.31e-998, 1.31e-998j
-11.609534773773414555 - 2.4615985095098398556e-2069j 5.88e-1000, 5.88e-1000j
-12.428675433919729811 + 5.913151880616502136e-2073j 7.26e-1002, 7.26e-1002j
-9.926052880765454393 + 1.7957518722127479002e-2066j 3.31e-997, 3.31e-997j
-10.558711754748694577 - 3.4604217553871466684e-2073j 4.59e-998, 4.59e-998j
-1.4490965895233053378 - 8.1684982558797205649e-2098j 8.76e-1012, 8.76e-1012j
-13.489347255723870127 - 1.7377960762593348567e-2089j 7.79e-1005, 7.79e-1005j
1.0693259078659559849 - 5.5997412592053317683e-2101j 8.74e-1014, 8.74e-1014j
-8.4843660807688419175 + 7.3684397153169545033e-2082j 3e-996, 3e-996j
-2.9263645536597399004 + 1.7308539158369448357e-2102j 2.88e-1004, 2.88e-1004j
-9.0419425189672695474 + 5.7877929384625671194e-2093j 1.63e-996, 1.63e-996j
-9.3295006620009277994 + 4.5358273551061620321e-2103j 1.09e-996, 1.09e-996j
-12.00200298657122261 - 1.5440766458081419293e-2117j 8.04e-1001, 8.04e-1001j
-1.0693259078659559849 + 6.2259755014338579976e-2133j 1.01e-1013, 1.01e-1013j
-0.88811750256253367035 + 1.5320531629477893903e-2134j 7.27e-1015, 7.27e-1015j
-9.6238901239691935554 + 1.9723196251333968969e-2114j 5.81e-997, 5.81e-997j
-12.908187500966365139 + 2.3774768783080623325e-2129j 3.97e-1003, 3.97e-1003j
-3.1646264004517797537 + 1.9564933884828261775e-2133j 7.41e-1004, 7.41e-1004j
-0.70673991102397831365 + 6.7885174675006905946e-2146j 6.68e-1016, 6.68e-1016j
-6.1747663347029431356 - 6.15081090450444821e-2125j 1.46e-997, 1.46e-997j
-4.7505039662432625641 + 8.8179431051954101228e-2141j 4.84e-1000, 4.84e-1000j
-10.237161907544437147 + 3.8165778249550862212e-2137j 1.37e-997, 1.37e-997j
0.88811750256253367035 - 3.5106235987620731643e-2171j 8.29e-1015, 8.29e-1015j
-7.4245339057704326501 + 1.2888702750825874546e-2150j 1.92e-996, 1.92e-996j
-1.2551527310423468231 - 6.3857639743043376287e-2182j 8.21e-1013, 8.21e-1013j
-6.6664670104660117931 - 1.9742605344098188622e-2164j 5.35e-997, 5.35e-997j
-6.419382591282156486 + 3.2567521439315544031e-2189j 2.84e-997, 2.84e-997j
-8.7604447186513183834 - 4.5732775917748655993e-2229j 2.19e-996, 2.19e-996j
-4.9833302245568576804 - 5.4263940816708387758e-2264j 1.44e-999, 1.44e-999j
-1.8579289724946339736 - 9.5726847296715950029e-2309j 8.85e-1010, 8.85e-1010j
-8.213166061109724224 - 1.4950455599950341444e-2297j 2.93e-996, 2.93e-996j
-5.9324484985156980773 - 1.7174404240819655001e-2336j 6.68e-998, 6.68e-998j
-11.241672484718744893 + 8.8187043390168680215e-2367j 3.1e-999, 3.1e-999j
-2.9899278943630500681 + 3.4051058301017567349e-2393j 5.34e-1004, 5.34e-1004j
-4.5192710191831587742 - 5.5017579642237456585e-2386j 1.37e-1000, 1.37e-1000j
-4.2895616337236207733 + 6.0040209149891315506e-2404j 4.11e-1001, 4.11e-1001j
-1.6506801238857845559 + 4.2801135629022322341e-2430j 7.86e-1011, 7.86e-1011j
-3.3855432781284968142 + 3.4148498231995846758e-2416j 2.12e-1003, 2.12e-1003j
-3.8345325314433831864 + 3.7739337824614858674e-2439j 3.05e-1002, 3.05e-1002j
0.52464762327529031788 + 3.1924332490269973027e-2488j 4.03e-1017, 4.03e-1017j
-2.2832506552235534748 + 3.3619660462535013908e-2468j 8.9e-1008, 8.9e-1008j
-7.9463835836425496153 + 1.4569760484794642743e-2518j 2.83e-996, 2.83e-996j
0.34484221454873728298 + 1.805521072370690126e-2644j 2.59e-1018, 2.59e-1018j
-0.52464762327529031788 - 4.6910699044304806213e-2643j 4.3e-1017, 4.3e-1017j
-2.0996011264233729169e-2648 - 5.5290693143192946194e-2649j 2.32e-2646, 2.32e-2646j
-5.4541126887358558191 + 2.7777628029741020228e-2622j 1.07e-998, 1.07e-998j
-7.6836213369996262221 - 2.9761105129335758811e-2706j 2.33e-996, 2.33e-996j
-2.7166709002873981457 - 1.5864524821702786847e-2749j 1.1e-1005, 1.1e-1005j
-3.609213199836183544 - 1.1926788007774360627e-2747j 7.57e-1003, 7.57e-1003j
0.70673991102397831365 + 1.8375153665200051881e-2806j 7.53e-1016, 7.53e-1016j
-4.0613239531173431814 + 3.4319074346438955074e-2786j 1.13e-1001, 1.13e-1001j
-0.34484221454873728298 + 8.0749521064524212172e-2857j 2.59e-1018, 2.59e-1018j
-2.0691626986869960821 - 3.0046091019628291102e-2835j 9.13e-1009, 9.13e-1009j
0.17011891758364476608 + 8.1367765005361096969e-2874j 1.5e-1019, 1.5e-1019j
-5.6922764034722333794 + 1.8482620232701611172e-2894j 3.02e-998, 3.02e-998j
-2.4994001356249370327 - 6.6240272838220282257e-2966j 9.73e-1007, 9.73e-1007j
-6.91620863943432204 + 2.5569029134843681027e-2995j 9.3e-997, 9.3e-997j
-5.2178340171465813101 + 1.6298550095441625086e-3032j 3.98e-999, 3.98e-999j
-7.1688186558445482346 + 3.4102984088918133183e-3054j 1.37e-996, 1.37e-996j
-0.17011891758364476608 + 1.0807005580468076281e-3087j 1.5e-1019, 1.5e-1019j

Weights

Weight (ball center) Error (ball radius)
2.635524576620035909e-56 - 4.9238822979507490617e-2106j 7.18e-322, 5.05e-818j
5.4618522823554293744e-47 + 4.893226505450238739e-2101j 5.22e-318, 3.67e-814j
8.8110085445006012435e-09 + 7.1626962747681027992e-2079j 7.81e-278, 5.5e-774j
6.3424472924037727192e-64 - 4.4774654330624876839e-2110j 1.48e-325, 1.04e-821j
0.0075735078760643029586 - 1.0797822572508115912e-2074j 2.38e-240, 1.67e-736j
5.6892938154513240558e-53 + 2.9690985684120668289e-2104j 6.87e-321, 4.83e-817j
2.0753013561878539835e-68 + 1.9325371836473748588e-2112j 9.71e-328, 6.83e-824j
0.00023697831399886534006 - 8.5678062138869517634e-2076j 1.97e-261, 1.38e-757j
0.0037446250540343988376 + 5.466184094893983325e-2075j 9.45e-249, 6.64e-745j
1.2655984017346415051e-73 - 3.5257700474735363274e-2115j 3.6e-330, 2.53e-826j
0.013685669157889135161 + 2.1252556146129429353e-2074j 7.63e-240, 5.37e-736j
7.6778186007238940471e-31 - 3.935190600158844316e-2092j 2.85e-312, 2.01e-808j
7.0100389889135773349e-21 - 3.3832996101323919844e-2086j 2.03e-304, 1.43e-800j
1.9138852459833852433e-05 - 8.5719482645966134936e-2076j 1.15e-270, 8.11e-767j
7.0557744186878641711e-50 - 1.3556504427279623315e-2102j 8.77e-321, 6.17e-817j
1.6122600079612296661e-14 - 4.184045453640593681e-2081j 2.42e-297, 1.7e-793j
4.9989384734163383009e-37 + 1.3650415944524502916e-2095j 2.03e-316, 1.43e-812j
6.2411364773694834267e-60 + 5.8196527133472606002e-2108j 1.6e-325, 1.13e-821j
3.7944659308575067985e-18 - 1.5650522374252166242e-2083j 3.66e-303, 2.57e-799j
8.4336368201324822925e-33 + 3.1065329079797368068e-2093j 2.52e-314, 1.77e-810j
1.0040522570313242429e-41 + 3.5553281612272495998e-2098j 3.99e-319, 2.81e-815j
2.8068024652545031421e-44 - 1.4418428519597179384e-2099j 3.37e-320, 2.37e-816j
1.9914632088913184136e-13 + 1.7189602038067892667e-2080j 1.62e-300, 1.14e-796j
2.5957199838445905781e-39 - 7.4817442595215939732e-2097j 3e-318, 2.11e-814j
0.022143987559460078548 - 4.0226407809243899848e-2074j 1.32e-255, 9.27e-752j
6.8741698954818802727e-24 - 8.3897465787157881748e-2088j 3.03e-311, 2.13e-807j
2.7889020013586291794e-07 + 2.6984509925651825267e-2078j 5.84e-290, 4.11e-786j
1.7541795217379253897e-10 - 1.6357424085326137616e-2079j 2.22e-297, 1.56e-793j
1.3220760208934673584e-06 + 4.1041249640542246833e-2078j 2.12e-288, 1.49e-784j
7.3527060965467908408e-35 - 2.1868747334699633392e-2094j 1.57e-317, 1.11e-813j
5.2474888510921980645e-08 - 1.7236815418812850742e-2078j 3.25e-292, 2.28e-788j
1.7596683924535270716e-19 + 9.8355949268666394894e-2085j 1.7e-308, 1.19e-804j
0.0016596534801504642878 - 2.813058291892129595e-2075j 7.33e-277, 5.15e-773j
2.0705975402264147567e-11 - 1.5594788475332547038e-2079j 1.09e-299, 7.69e-796j
7.0681166551963211288e-17 + 3.8506458306731086441e-2083j 1.86e-306, 1.31e-802j
3.5801125201743218914e-80 + 1.3224694289885122518e-2118j 1.12e-343, 7.89e-840j
5.6320492855764147843e-29 + 4.4558612399634112091e-2091j 2.17e-316, 1.53e-812j
1.3183527621384841371e-09 + 3.6451127199179787227e-2079j 1.4e-297, 9.87e-794j
2.1622394898330236742e-12 + 1.8840912699402265708e-2080j 1.21e-301, 8.51e-798j
5.4992911412984073286e-06 - 8.0857949507844705323e-2077j 2.6e-291, 1.83e-787j
0.00066109659742917311446 + 1.4987038110304960652e-2075j 3.32e-285, 2.33e-781j
3.9725984757488008709e-06 + 6.6978992168783030294e-2076j 4.1e-290, 2.88e-786j
7.6368110095523807815e-05 + 5.8731348683285273368e-2076j 7.04e-289, 4.95e-785j
3.3725423171185040232e-27 - 4.4375725349115527327e-2090j 4.87e-318, 3.42e-814j
1.6673845806266408794e-25 + 4.6546889228633864529e-2089j 4.1e-317, 2.88e-813j
2.3840838777671737191e-22 + 2.4944199344190104342e-2087j 6.3e-315, 4.43e-811j
1.1430734763589340536e-15 + 3.0993465008528123864e-2082j 2.79e-309, 1.97e-805j
5.6892938154513240558e-53 - 8.2999030105827025929e-2105j 2.77e-365, 1.95e-861j
6.2411364773694834267e-60 - 1.7837244008311005922e-2108j 4.83e-368, 3.4e-864j
2.0753013561878539835e-68 - 6.4779653361047262584e-2113j 3.18e-371, 2.24e-867j
2.8068024652545031421e-44 + 3.466758411398079114e-2100j 4.63e-363, 3.26e-859j
7.0557744186878641711e-50 + 3.6112462763603869605e-2103j 8.99e-365, 6.32e-861j
0.013685669157889135161 + 1.4872240958341078789e-2074j 8.75e-304, 6.15e-800j
3.5801125201743218914e-80 - 4.8836420171600152344e-2119j 4.64e-376, 3.27e-872j
0.032834902011675526701 + 6.9720655173052811374e-2074j 1.37e-295, 9.61e-792j
8.4336368201324822925e-33 - 5.545729733944703761e-2094j 1.9e-359, 1.33e-855j
1.9138852459833852433e-05 - 5.4465819552354982159e-2076j 4.05e-328, 2.85e-824j
4.9989384734163383009e-37 - 2.7628850582383162161e-2096j 2.78e-361, 1.95e-857j
2.5957199838445905781e-39 + 1.6079925242574911258e-2097j 2.93e-362, 2.06e-858j
6.3424472924037727192e-64 + 1.4351417197987621201e-2110j 6.7e-372, 4.72e-868j
0.032834902011675526701 + 5.3336916032952584345e-2074j 6.1e-307, 4.29e-803j
0.046338225454857423664 - 8.6107118880921479462e-2074j 5.69e-305, 4e-801j
1.0040522570313242429e-41 - 8.0926372713226226589e-2099j 2.08e-363, 1.46e-859j
1.2655984017346415051e-73 + 1.2376308970523262526e-2115j 6.87e-376, 4.84e-872j
5.4992911412984073286e-06 - 6.2988278395299716469e-2077j 1.71e-336, 1.2e-832j
0.062335518201361008122 + 1.2650796502892854939e-2073j 3.81e-309, 2.68e-805j
3.7944659308575067985e-18 + 1.0709532979015568069e-2085j 2.95e-355, 2.07e-851j
2.0705975402264147567e-11 + 1.7236349185635463103e-2081j 8.15e-349, 5.73e-845j
5.4618522823554293744e-47 - 1.2397450019938598276e-2101j 5.67e-366, 3.99e-862j
0.046338225454857423664 - 1.076866724369020886e-2073j 2.13e-313, 1.5e-809j
1.6673845806266408794e-25 - 6.1774848920069371682e-2090j 3.87e-360, 2.72e-856j
0.022143987559460078548 - 2.9438606772853144866e-2074j 3.22e-320, 2.27e-816j
7.0100389889135773349e-21 + 2.6812447084374111265e-2087j 8.41e-358, 5.91e-854j
1.7596683924535270716e-19 - 1.751938661156553094e-2086j 7.64e-357, 5.37e-853j
7.3527060965467908408e-35 + 4.1590872114846901375e-2095j 1.56e-363, 1.1e-859j
2.1622394898330236742e-12 - 3.8638594384338923936e-2082j 3.97e-353, 2.8e-849j
0.0037446250540343988376 + 3.5096947619006074083e-2075j 2.36e-334, 1.66e-830j
7.6778186007238940471e-31 + 6.6117102193424475133e-2093j 7.18e-363, 5.05e-859j
7.0681166551963211288e-17 - 6.1490257418291588888e-2085j 2.26e-356, 1.59e-852j
2.635524576620035909e-56 + 1.4421361576942472972e-2106j 6.33e-373, 4.45e-869j
3.9725984757488008709e-06 + 4.399070555956979204e-2076j 4.85e-344, 3.41e-840j
1.7541795217379253897e-10 - 7.4203498978843232127e-2081j 2.44e-352, 1.71e-848j
1.3183527621384841371e-09 + 3.1062681090343505512e-2080j 6.33e-352, 4.45e-848j
0.0075735078760643029586 - 7.2294509800584333327e-2075j 8.42e-338, 5.93e-834j
1.3220760208934673584e-06 + 1.0230338096802656434e-2077j 2.03e-348, 1.43e-844j
5.2474888510921980645e-08 + 5.2485299798254048471e-2079j 7.08e-351, 4.98e-847j
0.077780925525534640723 - 2.009628682728740366e-2073j 3.6e-335, 2.53e-831j
0.00066109659742917311446 + 9.0090773886078532238e-2076j 3.08e-344, 2.17e-840j
5.6320492855764147843e-29 - 7.1052763149603055721e-2092j 3.92e-365, 2.76e-861j
0.08893933240630260196 + 2.5580851738382683905e-2073j 7.25e-338, 5.1e-834j
0.077780925525534640723 - 1.7593620267603573506e-2073j 2.05e-338, 1.44e-834j
0.095428228118557150427 + 3.1856082217994179732e-2073j 6.65e-339, 4.68e-835j
1.6122600079612296661e-14 - 1.7060113199833942379e-2083j 3.63e-358, 2.55e-854j
3.3725423171185040232e-27 + 6.9316793696266136996e-2091j 1.21e-364, 8.51e-861j
7.6368110095523807815e-05 + 3.5142536940934948333e-2076j 4.37e-348, 3.07e-844j
2.7889020013586291794e-07 - 2.2154648442649261718e-2078j 2.23e-351, 1.57e-847j
0.062335518201361008122 + 1.5125400640222747277e-2073j 1.57e-341, 1.1e-837j
8.8110085445006012435e-09 - 1.2777318642261982791e-2079j 3.69e-353, 2.59e-849j
0.08893933240630260196 + 2.3435754697186853383e-2073j 8.13e-343, 5.73e-839j
0.0016596534801504642878 - 1.7403634868243176798e-2075j 2.09e-347, 1.47e-843j
0.094244821680817899891 - 3.0304421074867127269e-2073j 1.49e-343, 1.05e-839j
1.1430734763589340536e-15 + 3.3289776573924563972e-2084j 1.54e-359, 1.08e-855j
0.00023697831399886534006 - 5.075213520275815351e-2076j 3.11e-349, 2.2e-845j
2.3840838777671737191e-22 - 3.8233137366122471892e-2088j 3.29e-364, 2.33e-860j
1.9914632088913184136e-13 + 8.3096731516352454403e-2083j 1.04e-358, 7.01e-855j
6.8741698954818802727e-24 + 5.0575657587325811956e-2089j 4.15e-365, 2.95e-861j
0.094244821680817899891 - 2.9021667770028018539e-2073j 6.09e-348, 3.39e-844j

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