Rule: Q[1, 4, 42]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ 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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_3$:
  $t^{47}-\frac{6042082028238263961637701173651}{6062989709009127413615092763}\cdot t^{45}+\frac{52223877439453078662870319733319555}{115196804471173420858686762497}\cdot t^{43}-\frac{14398492116015867143560046342882102415}{115196804471173420858686762497}\cdot t^{41}+\frac{207237263468932259836752648757147139475}{8861292651628724681437443269}\cdot t^{39}-\frac{1469792988804031235541802727880437157345}{466383823769932877970391751}\cdot t^{37}+\frac{147745609997502383846464291221740937595515}{466383823769932877970391751}\cdot t^{35}-\frac{11323851931734135557003805728872894783589775}{466383823769932877970391751}\cdot t^{33}+\frac{670818858283552010834995489733360209668562950}{466383823769932877970391751}\cdot t^{31}-\frac{30957982830086420889173043112922729624563881750}{466383823769932877970391751}\cdot t^{29}+\frac{1116961238066997391441598922201489460036484142450}{466383823769932877970391751}\cdot t^{27}-\frac{31505624829557414791623352245407876144542439962650}{466383823769932877970391751}\cdot t^{25}+\frac{692489240475627237406400743648427641225665386441250}{466383823769932877970391751}\cdot t^{23}-\frac{11785446481001605849854289080450595393803895543661250}{466383823769932877970391751}\cdot t^{21}+\frac{153814795713475619434473245377640143018041727681893750}{466383823769932877970391751}\cdot t^{19}-\frac{1519082892546816319984743568448900918991471873869298750}{466383823769932877970391751}\cdot t^{17}+\frac{11152799106172287692772797742601924263831764719252231875}{466383823769932877970391751}\cdot t^{15}-\frac{59457406625701624494136965852498445155553264857578446875}{466383823769932877970391751}\cdot t^{13}+\frac{223033480663511672359435075630979650790966480231473715625}{466383823769932877970391751}\cdot t^{11}-\frac{563476573862874596760432912434651623236225866268436078125}{466383823769932877970391751}\cdot t^9+\frac{898893692825998097097524089690322801623793677594473778125}{466383823769932877970391751}\cdot t^7-\frac{816029399917821761606448883369480451411849857192597978125}{466383823769932877970391751}\cdot t^5+\frac{348029524649384212588888010645384486904261408217071609375}{466383823769932877970391751}\cdot t^3-\frac{44335989471845965337836263429333145906504114639289671875}{466383823769932877970391751}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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