Rule: Q[2, 3, 6, 16, 24]

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)
4.0000729252845649076 + 4.4117839453787882455e-943j 2.09e-243, 2.09e-243j
5.7315176002685958101 - 2.7730424267825725434e-955j 2.94e-244, 2.94e-244j
-7.937864439424572719 + 1.4506036225778887669e-962j 2.68e-247, 2.68e-247j
-4.6529242980124219822 - 3.5260021469732316537e-959j 2.13e-243, 2.13e-243j
-6.1872527365844323403 + 1.8664988074410782429e-962j 1.07e-244, 1.07e-244j
7.2542390775624442848 - 1.1227379257911109307e-961j 3.89e-246, 3.89e-246j
4.6529242980124219822 - 1.5876989749684368332e-965j 1.91e-243, 1.91e-243j
-5.7315176002685958101 - 4.641378496939120555e-979j 2.99e-244, 2.99e-244j
-3.5036073689616668479 + 1.9394239776587018197e-975j 1.12e-243, 1.12e-243j
6.6889615042667561023 + 8.3225127125778730262e-979j 2.62e-245, 2.62e-245j
-3.2137281525534003284 + 1.0645623779165823159e-987j 5.47e-244, 5.47e-244j
5.3205461080820075782 - 1.3714286151216816432e-985j 7.7e-244, 7.7e-244j
-2.2919835449503183599 - 2.4692042940010080109e-997j 1.1e-244, 1.1e-244j
6.1872527365844323403 - 2.2511517359893462305e-998j 1.01e-244, 1.01e-244j
7.937864439424572719 + 3.2247748459827146034e-1007j 2.65e-247, 2.65e-247j
2.3142743884833336815 - 4.8092474640925759274e-1000j 1.25e-244, 1.25e-244j
-2.1109759403485031626 - 5.3815378451154657844e-1004j 3.87e-246, 3.87e-246j
-4.3256200360048530098 - 1.5711161296145783979e-1000j 2.04e-243, 2.04e-243j
-7.2542390775624442848 - 1.3582702065497980816e-1004j 3.58e-246, 3.58e-246j
-5.3205461080820075782 - 5.6848886377203756765e-1002j 7.63e-244, 7.63e-244j
-4.0000729252845649076 - 7.6378906627636107278e-1002j 2.15e-243, 2.15e-243j
2.2919835449503183599 - 3.0906417996372050268e-1001j 1.08e-244, 1.08e-244j
2.7156176269150499178 - 3.7183697604798810695e-1004j 6.6e-245, 6.6e-245j
-2.3142743884833336815 + 7.7909019176250534816e-1018j 1.08e-244, 1.08e-244j
-6.6889615042667561023 + 2.4112388190746503745e-1018j 2.41e-245, 2.41e-245j
-1.7320508075688772935 - 2.4061867608954297279e-1020j 7.37e-248, 7.37e-248j
0.7071067811865475244 + 2.3895261327465879022e-1025j 1.74e-251, 1.74e-251j
-0.30858349852792099829 - 5.539643364259700585e-1026j 2.52e-253, 2.52e-253j
-1.3866480207208212553 + 9.4325043627012182395e-1022j 6.01e-249, 6.01e-249j
-3.7487098758283944347 - 3.5546621644047449791e-1017j 1.99e-243, 1.99e-243j
4.9662161004294137869 - 5.336544765071103167e-1016j 1.53e-243, 1.53e-243j
4.3256200360048530098 + 5.5616721574210402381e-1024j 1.97e-243, 1.97e-243j
1.0945422412614507352 - 2.6923165970449392383e-1038j 1.77e-249, 1.77e-249j
1.0095978244366004968 - 2.0820125080574219871e-1038j 8.88e-250, 8.88e-250j
-2.7156176269150499178 + 1.2744948955415982864e-1033j 6.38e-245, 6.38e-245j
-1.0945422412614507352 - 6.1105395961167038967e-1038j 1.73e-249, 1.73e-249j
3.7487098758283944347 - 1.1739703054791061553e-1030j 1.78e-243, 1.78e-243j
2.1109759403485031626 - 2.9361171050541507969e-1042j 4.23e-246, 4.23e-246j
3.5036073689616668479 + 5.3694933053402194658e-1038j 1.12e-243, 1.12e-243j
-0.47842841922329504798 - 2.4677335594450274505e-1052j 1.72e-252, 1.72e-252j
-0.7071067811865475244 + 2.9382412607377173011e-1051j 1.82e-251, 1.82e-251j
-2.9840214675649005304 + 5.5834367894690317695e-1045j 2.5e-244, 2.5e-244j
2.9840214675649005304 - 9.6879525074099389662e-1046j 2.22e-244, 2.22e-244j
1.7320508075688772935 + 1.8555480941751793162e-1058j 6.79e-248, 6.79e-248j
-4.9662161004294137869 - 1.1130539167771111405e-1057j 1.54e-243, 1.54e-243j
-1.0095978244366004968 - 6.4759897831731139789e-1064j 8.48e-250, 8.48e-250j
0.30858349852792099829 + 1.8701817005590667583e-1066j 2.52e-253, 2.52e-253j
1.3866480207208212553 - 7.1584511538113453737e-1065j 5.88e-249, 5.88e-249j
0.47842841922329504798 + 4.6296314679300838488e-1068j 1.87e-252, 1.87e-252j
3.2137281525534003284 - 1.1094123538581995011e-1071j 5.12e-244, 5.12e-244j
1.9306409095684038465e-1207 + 2.2890265109378010884e-1207j 1.53e-1205, 1.53e-1205j

Weights

Weight (ball center) Error (ball radius)
1.9076243936297357733e-08 - 7.2598797157445201146e-950j 1.34e-72, 9.82e-193j
1.3263170822299450641e-15 - 2.6797816730395116586e-957j 1.71e-80, 1.25e-200j
1.9233705001122433359e-28 + 6.601309315835108661e-967j 1.52e-88, 1.11e-208j
7.0337173284979020451e-11 - 6.1048381243003133775e-954j 1.19e-77, 8.7e-198j
6.3752890004970922727e-18 - 7.8331672544233269506e-960j 1.71e-83, 1.25e-203j
4.8080218570578803134e-24 + 1.5331519506525565559e-963j 1.59e-87, 1.17e-207j
7.0337173284979020451e-11 + 8.0914507566276223292e-953j 3.45e-78, 2.53e-198j
1.3263170822299450641e-15 + 4.7678677968690906405e-958j 1.91e-82, 1.4e-202j
7.5174841359475787875e-07 - 3.2638564731622038627e-950j 3.93e-74, 2.88e-194j
1.1052557510228534413e-20 - 3.2835891928308533215e-961j 5.39e-86, 3.96e-206j
4.9579457356280512384e-06 + 1.7884666429327192035e-949j 3e-73, 2.2e-193j
1.1036062170953150276e-13 + 1.3894252723589301633e-955j 1.26e-81, 9.24e-202j
-0.00624870613352464593 + 1.9681404707125685876e-946j 2.84e-69, 2.08e-189j
6.3752890004970922727e-18 + 3.6484895010665869027e-959j 1.67e-84, 1.22e-204j
1.9233705001122433359e-28 - 2.001274492428961603e-966j 5.73e-91, 4.21e-211j
0.0060182134893729696641 - 6.2973756466910021756e-946j 1.4e-71, 1.03e-191j
0.003260256987508858733 - 4.282622102628349305e-947j 1.99e-69, 1.46e-189j
1.4173107629338745462e-09 + 7.6282464284060393148e-953j 2.66e-80, 1.96e-200j
4.8080218570578803134e-24 - 4.4330841217568418893e-964j 3.32e-91, 2.44e-211j
1.1036062170953150276e-13 - 1.9684302137911784143e-956j 2.25e-84, 1.65e-204j
1.9076243936297357733e-08 - 1.051984155142678052e-951j 1.1e-79, 8.06e-200j
-0.00624870613352464593 + 7.2500017420953546256e-946j 1.73e-74, 1.27e-194j
0.00011284988462750824361 + 9.7793242893240310709e-948j 9.57e-78, 7.02e-198j
0.0060182134893729696641 - 1.6812674570073339778e-946j 4.18e-73, 3.06e-193j
1.1052557510228534413e-20 + 8.2600589761983576822e-962j 1.04e-89, 7.6e-210j
0.0098881408318278698513 + 3.9304758169335581657e-947j 1.6e-72, 1.18e-192j
0.10521453123221843319 + 1.5740667473937730838e-945j 8.63e-71, 6.34e-191j
0.13967355462774367298 + 1.6570151712644122547e-945j 5.79e-71, 4.25e-191j
0.027930583376020920242 - 1.3727480528770708996e-946j 2.95e-71, 2.16e-191j
9.5843649715398165362e-08 + 7.2878461673509771331e-951j 2.43e-79, 1.78e-199j
3.5633380900588297603e-12 - 4.2951459143766321706e-954j 2.34e-86, 1.71e-206j
1.4173107629338745462e-09 - 1.9508831595966587145e-951j 5.85e-85, 4.29e-205j
0.022556350325875501652 + 1.89920698974761341e-945j 2.72e-74, 2e-194j
0.04504617245631789742 - 2.2944215896964434088e-945j 8.77e-74, 6.44e-194j
0.00011284988462750824361 + 1.8704115087289315408e-948j 7.34e-79, 5.39e-199j
0.022556350325875501652 + 1.0831444581444371215e-945j 3.51e-76, 2.57e-196j
9.5843649715398165362e-08 + 2.2466284189701478679e-949j 2.86e-84, 2.1e-204j
0.003260256987508858733 - 1.3853874708866434784e-946j 6.87e-80, 5.05e-200j
7.5174841359475787875e-07 - 4.9330583338565651186e-949j 3.48e-84, 2.54e-204j
0.05594926374939012673 - 1.8162433921952864691e-945j 5.16e-77, 3.74e-197j
0.10521453123221843319 + 1.1011579822611180611e-945j 1.98e-77, 1.43e-197j
1.6734266526842175131e-05 - 6.0837546978326742655e-949j 6.46e-82, 4.67e-202j
1.6734266526842175131e-05 - 4.1818272834294249211e-948j 1.81e-83, 1.33e-203j
0.0098881408318278698513 + 9.9337539681239117915e-947j 3.7e-81, 2.67e-201j
3.5633380900588297603e-12 + 4.6281420323683025039e-955j 1.88e-88, 1.35e-208j
0.04504617245631789742 - 1.3696330512773078974e-945j 2.29e-78, 1.64e-198j
0.13967355462774367298 + 1.9340456484243370982e-945j 3.81e-80, 2.74e-200j
0.027930583376020920242 - 2.8294712723935377809e-946j 1.81e-81, 1.35e-201j
0.05594926374939012673 - 2.309730144510661496e-945j 2.95e-80, 2.12e-200j
4.9579457356280512384e-06 + 1.6407106709254618814e-948j 1.23e-84, 9.45e-205j
0.18115245760145640581 - 1.1279237700579360134e-945j 1.42e-80, 9.53e-201j

Download

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