Rule: Q[2, 3, 4, 20, 38]

Type

This rule is of Hermite (probabilists') 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)
35.089329256056931947 - 4.1428358837168536983e-571j 3.66e-251, 3.66e-251j
-35.089329256056931947 - 5.7986451977170989524e-571j 3.71e-251, 3.71e-251j
-9.7853185866786381824 - 5.7699765321353585166e-558j 6.51e-241, 6.51e-241j
-13.348752773977650803 + 8.4795779954235836639e-575j 5.32e-245, 5.32e-245j
-7.9377211407362450961 + 1.0587603361516740807e-590j 1.98e-239, 1.98e-239j
12.431327439076438382 + 4.9621510764083172697e-606j 1.07e-243, 1.07e-243j
-10.370535998319868931 + 1.1146476243493975625e-600j 2.26e-241, 2.26e-241j
-10.994597412434434024 + 6.670732061001927547e-607j 5.46e-242, 5.46e-242j
11.671941076182134531 + 1.6736936158317273925e-611j 9.72e-243, 9.72e-243j
7.6415162942837753237 + 5.9486156751831911589e-607j 1.32e-239, 1.32e-239j
-12.431327439076438382 + 8.7900597085232728894e-612j 1.08e-243, 1.08e-243j
6.7508691875889670917 + 1.120759483167703652e-609j 3.03e-240, 3.03e-240j
8.7049483044122572353 - 1.7147687026639681785e-608j 4.66e-240, 4.66e-240j
-1.5093152835436173382 + 4.1662195830213153996e-621j 3.48e-248, 3.48e-248j
-3.4396056846873525102 + 2.1480399124341343017e-618j 3.74e-244, 3.74e-244j
10.370535998319868931 + 1.1350341427442528454e-611j 1.99e-241, 1.99e-241j
7.9377211407362450961 + 3.4557405181494994296e-617j 1.93e-239, 1.93e-239j
-9.2310562487337185333 + 4.1215359932197724967e-641j 1.64e-240, 1.64e-240j
-7.6415162942837753237 + 4.2603354482413407478e-669j 1.28e-239, 1.28e-239j
-11.671941076182134531 - 2.0541904519027975511e-682j 1.01e-242, 1.01e-242j
1.6306719413090068156 - 1.0293254373645119804e-693j 4.87e-248, 4.87e-248j
2.8067118346786341233 - 6.2319558193981078166e-692j 1.33e-245, 1.33e-245j
10.994597412434434024 - 1.3142077226925191433e-686j 5.36e-242, 5.36e-242j
13.348752773977650803 - 8.5379988052067222607e-691j 5.37e-245, 5.37e-245j
-3.7932353000477464006 + 4.0366951687279961722e-688j 1.72e-243, 1.72e-243j
9.2310562487337185333 + 7.3782372718822819845e-685j 1.78e-240, 1.78e-240j
1 + 8.9031269943298068469e-699j 1.06e-250, 1.06e-250j
4.8270887717542989415 - 2.317830014101168402e-689j 7.29e-242, 7.29e-242j
4.1467468850046227486 - 6.3116192859871113057e-693j 7.85e-243, 7.85e-243j
-1 - 7.9781151350243701279e-702j 1.01e-250, 1.01e-250j
-5.5733350096591653341 + 4.9424873272551718181e-690j 4.84e-241, 4.84e-241j
1.5093152835436173382 - 5.4209429652502433438e-710j 3.3e-248, 3.3e-248j
0.69200566706654006968 - 4.7014190584354002724e-714j 4.38e-252, 4.38e-252j
-3.1198393628237582149 - 1.7269722575402679891e-706j 8.32e-245, 8.32e-245j
-4.1467468850046227486 + 5.6411139362125694847e-701j 8.14e-243, 8.14e-243j
-5.196616252964635271 + 2.2780916922833243768e-706j 2.03e-241, 2.03e-241j
6.3339346458873296653 - 9.2596075506947084234e-714j 2.08e-240, 2.08e-240j
5.196616252964635271 - 8.9715378972373624299e-719j 2.03e-241, 2.03e-241j
-8.2213128589847445729 - 9.8752045155605748994e-721j 1.27e-239, 1.27e-239j
5.5733350096591653341 - 7.3310591003561298769e-731j 5.09e-241, 5.09e-241j
-1.6306719413090068156 - 1.322379018358246348e-738j 4.71e-248, 4.71e-248j
-7.1937531631902611416 - 3.3613097868735140998e-728j 5.53e-240, 5.53e-240j
5.9469334613848628595 - 1.477726567885123629e-734j 1.06e-240, 1.06e-240j
8.2213128589847445729 - 4.9515529236142856747e-733j 1.3e-239, 1.3e-239j
-5.9469334613848628595 + 5.0839006717943210191e-733j 1.03e-240, 1.03e-240j
-6.3339346458873296653 + 7.0336437660890548937e-743j 2.07e-240, 2.07e-240j
-4.4824559233115378209 + 2.265927498629577924e-753j 2.75e-242, 2.75e-242j
-8.7049483044122572353 - 4.3473524074707477389e-754j 4.37e-240, 4.37e-240j
2.4494897427831780982 - 1.3423262366644780979e-772j 1.64e-246, 1.64e-246j
3.7932353000477464006 - 6.2766671491029419909e-770j 1.75e-243, 1.75e-243j
2.0627724124368029371 - 4.1741595294705313791e-774j 1.4e-247, 1.4e-247j
-2.0627724124368029371 - 1.9419686714385855539e-773j 1.49e-247, 1.49e-247j
7.1937531631902611416 - 1.4492599717329076523e-766j 5.32e-240, 5.32e-240j
4.4824559233115378209 + 3.2223057505429820116e-768j 2.74e-242, 2.74e-242j
-4.8270887717542989415 - 3.1109487815110422916e-765j 7.76e-242, 7.76e-242j
-3.2607056433698988043e-813 - 1.5649483572135644862e-812j 1.07e-810, 1.07e-810j
-0.69200566706654006968 + 5.2551707351384018943e-789j 4.61e-252, 4.61e-252j
-2.8067118346786341233 - 2.8142866003182420381e-780j 1.34e-245, 1.34e-245j
3.4396056846873525102 - 2.860494676228203384e-782j 3.77e-244, 3.77e-244j
1.3828023367484503294 + 5.7107074449316252764e-787j 7.72e-249, 7.72e-249j
-6.7508691875889670917 + 8.5043783150870465901e-776j 3.46e-240, 3.46e-240j
-2.4494897427831780982 - 3.5429656318469624556e-798j 1.53e-246, 1.53e-246j
-0.36144413319501211167 - 6.3373006512515747085e-804j 1.79e-253, 1.79e-253j
9.7853185866786381824 - 9.3542015312090718456e-790j 6.72e-241, 6.72e-241j
0.36144413319501211167 - 2.1564497538958197791e-814j 1.79e-253, 1.79e-253j
3.1198393628237582149 - 1.2275537423930468389e-805j 8.25e-245, 8.25e-245j
-1.3828023367484503294 + 2.0045051865817024575e-810j 8.99e-249, 8.99e-249j

Weights

Weight (ball center) Error (ball radius)
2.785275951150608445e-93 - 3.3950301928704331685e-623j 3.34e-89, 1.46e-208j
2.785275951150608445e-93 + 6.0208156845619322931e-623j 2.28e-89, 9.98e-209j
3.6601822705262631443e-22 - 1.4305436953338913387e-578j 1.8e-53, 7.89e-173j
8.567991874357843441e-40 - 6.1664005173479681169e-591j 1.23e-62, 5.38e-182j
1.4162081140766194707e-15 - 5.1946292323531773502e-574j 1.07e-48, 4.7e-168j
9.0379070570559663919e-35 - 9.2844478760047207259e-589j 2.71e-63, 1.19e-182j
1.0651285578707162928e-24 - 6.949479198857119289e-581j 1.77e-55, 7.76e-175j
1.4559659898010283169e-27 + 4.686875042395690167e-583j 2.43e-57, 1.07e-176j
7.417534674625279177e-31 + 2.2966873921466430546e-586j 2.72e-62, 1.19e-181j
3.5538033152125512833e-14 + 2.0343791232704626462e-574j 2.44e-52, 1.07e-171j
9.0379070570559663919e-35 + 7.7954876008389096414e-588j 2.47e-62, 1.08e-181j
2.1868421776958004908e-11 + 9.8993836521639598232e-573j 7.67e-50, 3.36e-169j
7.1548964561875206235e-18 - 1.8300504001988064885e-577j 3.81e-56, 1.67e-175j
-0.073201111599121128131 - 1.1970640179808773904e-563j 3.88e-17, 1.7e-136j
0.00036654626287084199826 - 1.7867268544041296043e-566j 5.34e-36, 2.34e-155j
1.0651285578707162928e-24 + 2.017754301540094429e-582j 6.09e-61, 2.67e-180j
1.4162081140766194707e-15 - 5.4153146694510888708e-575j 1.24e-53, 5.44e-173j
6.7586986454939268658e-20 + 1.5999114263880302431e-577j 4.49e-57, 1.97e-176j
3.5538033152125512833e-14 + 1.6537340776376710025e-573j 9.8e-54, 4.3e-173j
7.417534674625279177e-31 - 2.6121080402618478935e-585j 1.15e-62, 5.04e-182j
0.069472865629610071582 + 3.9521451514648906236e-564j 1.17e-25, 5.14e-145j
0.0025938446628129116082 - 4.7991700008521652413e-566j 9.78e-37, 4.29e-156j
1.4559659898010283169e-27 - 2.7275080168631655323e-584j 1.58e-63, 6.91e-183j
8.567991874357843441e-40 + 9.498355077034179755e-592j 4.67e-70, 2.05e-189j
0.0001077078376891340157 + 5.9907114732653085578e-567j 2.86e-44, 1.25e-163j
6.7586986454939268658e-20 + 4.6631950378011775084e-579j 1.53e-59, 6.72e-179j
0.078207983178214447505 - 2.2897468580715269422e-564j 1.3e-25, 5.71e-145j
1.246638545278869566e-06 - 6.5279087366328635204e-569j 1.56e-49, 6.85e-169j
2.5301551857938925715e-05 - 8.4368804423963480025e-568j 5.36e-47, 2.35e-166j
0.078207983178214447505 - 2.8110135225596009121e-564j 1.58e-27, 6.91e-147j
2.6879632694064045325e-08 - 9.8662606498812704675e-570j 2.53e-53, 1.11e-172j
-0.073201111599121128131 - 8.7713385672402264656e-564j 1.86e-31, 8.18e-151j
0.097171273991847358606 + 2.1070037238630224618e-564j 5.42e-28, 2.38e-147j
0.00093239360471970490642 + 4.4718512130546492627e-566j 1.83e-43, 8.04e-163j
2.5301551857938925715e-05 - 2.0846266912830599057e-567j 3.59e-48, 1.58e-167j
2.0552909176214668911e-07 + 4.4484276754028401401e-569j 2.62e-52, 1.15e-171j
3.108345058357581826e-10 - 7.7494129849665771537e-572j 5.5e-56, 2.41e-175j
2.0552909176214668911e-07 + 1.3624749188913840283e-569j 2.02e-53, 8.84e-173j
3.6523513152007033881e-16 + 8.5256878503943974671e-575j 2.16e-61, 9.46e-181j
2.6879632694064045325e-08 - 2.705740289227067077e-570j 9.17e-55, 4.02e-174j
0.069472865629610071582 + 5.5327537263646092173e-564j 2.33e-40, 1.02e-159j
1.042562831955829649e-12 - 8.0409807052306125023e-573j 7.08e-60, 3.1e-179j
3.1368558240494872432e-09 + 5.0193189409354841107e-571j 6.68e-56, 2.93e-175j
3.6523513152007033881e-16 + 7.4051744052097083743e-576j 2.84e-61, 1.24e-180j
3.1368558240494872432e-09 + 2.0572503308242811908e-570j 8.25e-58, 3.62e-177j
3.108345058357581826e-10 - 3.6192655598835413296e-571j 5.74e-59, 2.52e-178j
5.7707136456448003751e-06 + 6.9982294349724597227e-568j 8.38e-55, 3.68e-174j
7.1548964561875206235e-18 - 3.1320854413765109251e-576j 3.87e-64, 1.7e-183j
0.0074660908892178015881 + 1.0034441121151365221e-565j 1.81e-51, 7.92e-171j
0.0001077078376891340157 + 2.6436424963538772479e-567j 1.94e-55, 8.49e-175j
0.018820091354086589164 - 2.8852727931608144621e-565j 1.66e-50, 7.27e-170j
0.018820091354086589164 - 4.4266455440128773775e-565j 1.33e-51, 5.84e-171j
1.042562831955829649e-12 - 1.2273184231507675465e-573j 4.81e-62, 2.11e-181j
5.7707136456448003751e-06 + 2.6010117803871606031e-568j 1.52e-56, 6.66e-176j
1.246638545278869566e-06 - 1.923841072699618419e-568j 2.39e-57, 1.05e-176j
0.14621905982839787175 + 1.6678042297669528654e-564j 1.26e-50, 5.53e-170j
0.097171273991847358606 + 2.4276918009881001294e-564j 4.9e-51, 2.15e-170j
0.0025938446628129116082 - 8.6595070901045716387e-566j 1.99e-54, 8.7e-174j
0.00036654626287084199826 - 8.5732480728643846676e-567j 7.56e-56, 3.31e-175j
0.093762008436540062668 + 6.1912873234938026232e-564j 3.28e-51, 1.44e-170j
2.1868421776958004908e-11 + 5.3946546932305863981e-572j 7.73e-62, 3.4e-181j
0.0074660908892178015881 + 1.6735595448457061533e-565j 1.26e-54, 5.52e-174j
0.13115822105390130861 - 1.9260010652705628201e-564j 9.41e-53, 4.17e-172j
3.6601822705262631443e-22 - 1.0791251003838179726e-580j 2.27e-70, 1e-189j
0.13115822105390130861 - 1.7887865063441159753e-564j 2.55e-53, 1.17e-172j
0.00093239360471970490642 + 2.3096990729923860888e-566j 1.02e-55, 4.47e-175j
0.093762008436540062668 + 8.2290879831424931225e-564j 2.65e-53, 1.15e-172j

Download

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