Rule: Q[4, 18, 47]

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.

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)
0.99799761091448144824 - 1.3467617634582036788e-853j 6.19e-231, 6.19e-231j
0.98779804393346455757 - 5.7660748499459096822e-855j 6.41e-231, 6.41e-231j
-0.94095882085785033359 + 1.2150604831221523599e-857j 1.18e-231, 1.18e-231j
-0.99799761091448144824 + 1.4840757326861505596e-860j 6.17e-231, 6.17e-231j
0.92396019027290009586 + 1.599580460269093693e-881j 6.25e-232, 6.25e-232j
0.94095882085785033359 - 1.08589236385684034e-880j 1.2e-231, 1.2e-231j
0.99976592029801222522 - 1.5171492315474621141e-879j 2.45e-231, 2.45e-231j
-0.92396019027290009586 + 1.3370374155810898135e-884j 6.02e-232, 6.02e-232j
0.99402078285642610617 - 7.444881502629819942e-884j 7.23e-231, 7.23e-231j
-0.99976592029801222522 - 1.2233821681124256756e-881j 2.55e-231, 2.55e-231j
0.86113631159405257522 + 1.6375945900852708067e-906j 3.28e-233, 3.28e-233j
0.96869901960587075322 - 1.460639638056226225e-901j 3.63e-231, 3.63e-231j
-0.86113631159405257522 - 1.3373566519867380521e-904j 3.39e-233, 3.39e-233j
-0.88398468861339585517 - 5.9299071568038620011e-903j 1.03e-232, 1.03e-232j
-0.98779804393346455757 - 3.2912103659820120237e-909j 6.29e-231, 6.29e-231j
0.83647389364883225915 - 7.5666710790429994888e-936j 1.05e-233, 1.05e-233j
0.90494825076830645998 + 1.8936652976391198692e-933j 2.53e-232, 2.53e-232j
-0.99402078285642610617 + 1.64517386614034195e-932j 6.89e-231, 6.89e-231j
-0.78200094102074097978 + 1.2093107634850680757e-945j 7.71e-235, 7.71e-235j
-0.90494825076830645998 - 2.3843634743215705592e-942j 2.7e-232, 2.7e-232j
0.88398468861339585517 + 7.3102288535680389745e-944j 9.79e-233, 9.79e-233j
0.75233843743415970331 + 9.7049745707950230266e-947j 1.67e-235, 1.67e-235j
-0.1615542932426313501 + 3.9492800743881321929e-963j 4.82e-251, 4.82e-251j
-0.83647389364883225915 + 1.2999024863991345466e-943j 1.07e-233, 1.07e-233j
-0.81007069922651868812 - 3.8309248137484164788e-944j 2.9e-234, 2.9e-234j
0.97934776560959164277 + 5.5906988524682525339e-942j 5.3e-231, 5.3e-231j
0.72115559040597019372 + 3.6198488992876851605e-947j 3.58e-236, 3.58e-236j
0.81007069922651868812 + 3.6156605075994183367e-945j 2.84e-234, 2.84e-234j
-0.95588830445545680343 - 4.9444622078241817447e-940j 2.2e-231, 2.2e-231j
-0.61917244445806933852 + 4.3873601729579439522e-953j 1.3e-238, 1.3e-238j
-0.97934776560959164277 + 8.4632640796714558281e-944j 5.14e-231, 5.14e-231j
0.78200094102074097978 + 3.735251761346032194e-963j 7.76e-235, 7.76e-235j
0.68852261044466735796 - 2.3679183605075283303e-966j 5.59e-237, 5.59e-237j
-0.023200993046175310243 + 7.2600358828946561583e-983j 6.09e-255, 6.09e-255j
-0.72115559040597019372 - 3.6896779354487636585e-963j 3.29e-236, 3.29e-236j
-0.75233843743415970331 - 4.3194722052958011661e-962j 1.66e-235, 1.66e-235j
0.25198408513010750952 + 2.6231281732860981957e-977j 2.17e-248, 2.17e-248j
0.58258021317866156543 - 1.4898791317822799259e-968j 1.7e-239, 1.7e-239j
0.023200993046175310243 - 6.0889500912655789112e-983j 6.09e-255, 6.09e-255j
-0.96869901960587075322 + 4.4885516010133044926e-963j 3.57e-231, 3.57e-231j
-0.58258021317866156543 + 7.9710022295913661168e-973j 1.57e-239, 1.57e-239j
1.6552999922072976111e-1009 + 1.0943182750517503885e-1009j 1.37e-1007, 1.37e-1007j
0.65450686829818863455 + 1.2879552965290801729e-970j 9.19e-238, 9.19e-238j
0.54478881275121826226 + 2.6559454192004424738e-974j 1.79e-240, 1.79e-240j
0.61917244445806933852 + 4.4243470023234235427e-972j 1.39e-238, 1.39e-238j
-0.54478881275121826226 - 1.4090860445360009879e-973j 1.78e-240, 1.78e-240j
-0.68852261044466735796 - 3.970780607586691353e-971j 5.45e-237, 5.45e-237j
-0.11568533877813063942 + 1.8178859332867485065e-985j 2.36e-252, 2.36e-252j
0.50585648059320992835 - 5.4077800806310365903e-974j 1.98e-241, 1.98e-241j
0.20702313934899688624 + 3.1418656114933446279e-983j 1.15e-249, 1.15e-249j
-0.65450686829818863455 + 8.1665162768206506472e-972j 1.07e-237, 1.07e-237j
-0.50585648059320992835 + 7.9656634209898592936e-975j 1.75e-241, 1.75e-241j
0.95588830445545680343 + 5.5373925882303231406e-985j 2.28e-231, 2.28e-231j
0.46584324601871858403 + 1.5173018990541653643e-998j 1.62e-242, 1.62e-242j
0.42481282961461244487 + 2.8118693353643316452e-999j 1.27e-243, 1.27e-243j
-0.25198408513010750952 + 1.1548511834456759817e-1004j 2.08e-248, 2.08e-248j
-0.46584324601871858403 + 9.7553739219109785581e-999j 1.63e-242, 1.63e-242j
-0.42481282961461244487 - 1.0590339978986319843e-999j 1.29e-243, 1.29e-243j
0.11568533877813063942 + 2.0298177913282276852e-1008j 2.4e-252, 2.4e-252j
0.38283393022823750682 - 1.1644950324466453786e-1000j 9.13e-245, 9.13e-245j
0.1615542932426313501 + 3.457485489564253478e-1007j 5.21e-251, 5.21e-251j
-0.2963351128990086238 + 4.6306985822535861706e-1004j 3.72e-247, 3.72e-247j
-0.3399810435848562648 - 4.0699023877954408731e-1002j 6.33e-246, 6.33e-246j
0.069528472770917187352 - 1.1182214724187889512e-1009j 1.09e-253, 1.09e-253j
0.3399810435848562648 + 4.4515626062785075721e-1002j 6.26e-246, 6.26e-246j
0.2963351128990086238 - 2.00119473888580059e-1003j 3.86e-247, 3.86e-247j
-0.069528472770917187352 + 6.7798787587261814893e-1010j 1.07e-253, 1.07e-253j
-0.38283393022823750682 + 7.6430160983364472802e-1001j 9.88e-245, 9.88e-245j
-0.20702313934899688624 + 6.2596462489291700911e-1006j 1.07e-249, 1.07e-249j

Weights

Weight (ball center) Error (ball radius)
0.0028535177625221445052 + 9.3714905938135203121e-855j 2.22e-33, 4.17e-141j
0.0073406653106221298968 + 6.6657968687202250121e-854j 1.05e-33, 1.96e-141j
0.015972853275805668702 + 6.8801810510278305654e-856j 1.1e-35, 2.07e-143j
0.0028535177625221445052 + 2.0358514927767067043e-856j 1.86e-36, 3.5e-144j
0.018015095909886786887 - 2.0830499184949923284e-854j 1.74e-34, 3.27e-142j
0.015972853275805668702 + 2.3649759622792819509e-854j 1.87e-34, 3.5e-142j
0.0007622934086987297118 + 8.4367860868389549169e-854j 3.87e-34, 7.27e-142j
0.018015095909886786887 - 8.0830539711523799383e-856j 6.36e-38, 1.19e-145j
0.0051015170936402010945 - 1.3103659744380983469e-853j 3.96e-34, 7.44e-142j
0.0007622934086987297118 - 7.8243045710878585623e-857j 3.87e-38, 7.26e-146j
0.023767453111054523014 + 1.6915129610952617662e-854j 1.28e-37, 2.4e-145j
0.011736385286078254943 + 3.5291623471458515294e-854j 1.71e-35, 3.2e-143j
0.023767453111054523014 + 1.2439454299835537837e-855j 2.47e-39, 4.63e-147j
0.021917480015272193894 - 1.0727642115044841501e-855j 4.3e-39, 8.07e-147j
0.0073406653106221298968 + 3.6035073472772979176e-856j 2.73e-39, 5.13e-147j
0.025545145624840912821 - 1.6429906353162945766e-854j 3.65e-40, 6.86e-148j
0.019998490137445824253 + 1.8961502723013697226e-854j 4.21e-39, 7.9e-147j
0.0051015170936402010945 - 2.8802133274118086415e-856j 7.95e-39, 1.49e-146j
0.028878344800886534875 - 1.9539047364364614324e-855j 2.05e-42, 3.84e-150j
0.019998490137445824253 + 9.2788195488853302051e-856j 4.22e-40, 7.92e-148j
0.021917480015272193894 - 1.7719315302385795871e-854j 1.18e-39, 2.21e-147j
0.030434582871221653108 + 1.6188239552962006667e-854j 2.87e-43, 5.39e-151j
0.045687276893890177462 - 2.547237463419300145e-854j 1.9e-46, 3.56e-154j
0.025545145624840912821 - 1.4450715401977403016e-855j 6.72e-42, 1.26e-149j
0.027248851747024722481 + 1.6803044774837433763e-855j 1.88e-42, 3.52e-150j
0.0095550137128018212956 - 4.9297728059637032111e-854j 2.48e-39, 4.65e-147j
0.031919398504183638457 - 1.6361432443040431851e-854j 2.17e-44, 4.07e-152j
0.027248851747024722481 + 1.6183238597829183938e-854j 1.16e-42, 2.17e-150j
0.013877840852430999522 - 5.8179880839336682922e-856j 8.77e-43, 1.65e-150j
0.035973238085194428562 + 4.0378809181502505579e-855j 2.47e-48, 4.63e-156j
0.0095550137128018212956 - 4.3102773034594091592e-856j 1.01e-42, 1.9e-150j
0.028878344800886534875 - 1.6117304082758070792e-854j 1.05e-43, 1.97e-151j
0.033335324536240162633 + 1.660908483305972363e-854j 4.41e-46, 8.29e-154j
0.046367685321970151749 + 1.9925210865040768368e-853j 4.4e-51, 8.26e-159j
0.031919398504183638457 - 2.6326894127096703954e-855j 2.61e-47, 4.89e-155j
0.030434582871221653108 + 2.2700415156145318858e-855j 2.02e-46, 3.8e-154j
0.044672445102141707343 - 2.5656782305702905084e-854j 2.86e-52, 5.36e-160j
0.037201483382300507966 - 1.7614462393018495046e-854j 3.39e-50, 6.37e-158j
0.046367685321970151749 + 2.0873970989240767024e-853j 3.29e-52, 6.18e-160j
0.011736385286078254943 + 5.0463697814662449661e-856j 5.61e-45, 1.05e-152j
0.037201483382300507966 - 4.6272560429728941664e-855j 3.98e-51, 7.47e-159j
3.0360513572022561672e-05 - 3.2011038251097443613e-853j 5.39e-52, 1.01e-159j
0.034685480045323957153 - 1.6909368669587470942e-854j 1.46e-49, 2.74e-157j
0.038371649566503902668 + 1.8014928035794730704e-854j 7.4e-52, 1.39e-159j
0.035973238085194428562 + 1.7246926500353860093e-854j 1.65e-50, 3.09e-158j
0.038371649566503902668 + 5.2897426693993830149e-855j 3.77e-53, 7.08e-161j
0.033335324536240162633 + 3.0456239203616271688e-855j 3.73e-51, 7e-159j
0.046031917351034988618 + 3.6855923148207047398e-854j 1.11e-54, 2.09e-162j
0.039483042339093330755 - 1.8463758335041874778e-854j 2.81e-53, 5.27e-161j
0.045232424960537857076 + 2.9303802558211047273e-854j 1.99e-55, 3.73e-163j
0.034685480045323957153 - 3.5126018702053376253e-855j 3.3e-52, 6.2e-160j
0.039483042339093330755 - 6.0399798956638369914e-855j 7.34e-55, 1.38e-162j
0.013877840852430999522 - 2.8028901445832518978e-854j 7.56e-51, 1.42e-158j
0.040532827662937591943 + 1.8991077921593905076e-854j 8.74e-55, 1.64e-162j
0.041516568080128995673 - 1.9644722431724558577e-854j 1.09e-55, 2.05e-163j
0.044672445102141707343 - 1.5310052555176716672e-854j 5.82e-58, 1.09e-165j
0.040532827662937591943 + 6.9015212317980034386e-855j 7.8e-57, 1.46e-164j
0.041516568080128995673 - 7.9115820593598711307e-855j 1.26e-57, 2.37e-165j
0.046031917351034988618 + 4.6523948590198125189e-854j 1.43e-58, 2.68e-166j
0.042428825374431031599 + 2.0496020277699219144e-854j 2.69e-58, 5.05e-166j
0.045687276893890177462 - 3.5315514234693271351e-854j 1.29e-58, 2.42e-166j
0.044013740865685878766 + 1.2617059008049717277e-854j 5.43e-60, 1.02e-167j
0.04326346732680240259 - 1.0645910264160908309e-854j 4.52e-60, 8.49e-168j
0.046262493424580176705 - 7.3290144866246777774e-854j 2.6e-59, 4.89e-167j
0.04326346732680240259 - 2.165172634220518063e-854j 3.5e-60, 6.57e-168j
0.044013740865685878766 + 2.3278680196712741933e-854j 3.04e-60, 5.71e-168j
0.046262493424580176705 - 6.3740674445367856704e-854j 8.63e-61, 1.62e-168j
0.042428825374431031599 + 9.128645686054072397e-855j 5.71e-62, 1.09e-169j
0.045232424960537857076 + 1.9232542274928769987e-854j 1.08e-61, 2e-169j

Download

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