Rule: Q[2, 3, 6, 20]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^{11}-\frac{6923}{164}\cdot t^9+\frac{97479}{164}\cdot t^7-\frac{566685}{164}\cdot t^5+\frac{1313235}{164}\cdot t^3-\frac{418635}{82}\cdot t$
• $P_4$:
  $t^{31}-\frac{121921938457464510034469253163056449697836728231}{261532353574196499978585172820869754275211148}\cdot t^{29}+\frac{46721345774014034094114901782926188977659229853481}{523064707148392999957170345641739508550422296}\cdot t^{27}-\frac{7671336076773682666951258788997282210217001072248115}{813656211119722444377820537664928124411768016}\cdot t^{25}+\frac{929263510475282351885815567247020275074277395423463225}{1511075820650913110987380998520580802478997744}\cdot t^{23}-\frac{277433414685348288781589388900373518765355616033832188925}{10577530744556391776911666989644065617352984208}\cdot t^{21}+\frac{1137620377287397238822112648626688114672403182510008805975}{1511075820650913110987380998520580802478997744}\cdot t^{19}-\frac{2781209059042065986072630989654046194029486376889037714975}{188884477581364138873422624815072600309874718}\cdot t^{17}+\frac{148339151584349410226503876051374268756948982602247441719125}{755537910325456555493690499260290401239498872}\cdot t^{15}-\frac{1335337535407712069995177645993009407403524315341953063631625}{755537910325456555493690499260290401239498872}\cdot t^{13}+\frac{152791988285748761332482382324727177349994343611564893873375}{14529575198566472221032509601159430793067286}\cdot t^{11}-\frac{4635584095347505642223792677587578908012764570708037999279125}{116236601588531777768260076809275446344538288}\cdot t^9+\frac{10556175685090291234201524157913883859275654096455353941608625}{116236601588531777768260076809275446344538288}\cdot t^7-\frac{13063732950334203429399596854206267330900742447866011205541875}{116236601588531777768260076809275446344538288}\cdot t^5+\frac{7332115608620337099121646950355075119657811815644263925211875}{116236601588531777768260076809275446344538288}\cdot t^3-\frac{613534018006080977160851631739772482956498672166138016604375}{58118300794265888884130038404637723172269144}\cdot t$

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.