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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{11}-\frac{6923}{82}\cdot t^9+\frac{97479}{164}\cdot t^7-\frac{566685}{328}\cdot t^5+\frac{1313235}{656}\cdot t^3-\frac{418635}{656}\cdot t$
• $P_4$:
  $4\cdot t^{31}-\frac{121921938457464510034469253163056449697836728231}{130766176787098249989292586410434877137605574}\cdot t^{29}+\frac{46721345774014034094114901782926188977659229853481}{523064707148392999957170345641739508550422296}\cdot t^{27}-\frac{7671336076773682666951258788997282210217001072248115}{1627312422239444888755641075329856248823536032}\cdot t^{25}+\frac{929263510475282351885815567247020275074277395423463225}{6044303282603652443949523994082323209915990976}\cdot t^{23}-\frac{277433414685348288781589388900373518765355616033832188925}{84620245956451134215293335917152524938823873664}\cdot t^{21}+\frac{1137620377287397238822112648626688114672403182510008805975}{24177213130414609775798095976329292839663963904}\cdot t^{19}-\frac{2781209059042065986072630989654046194029486376889037714975}{6044303282603652443949523994082323209915990976}\cdot t^{17}+\frac{148339151584349410226503876051374268756948982602247441719125}{48354426260829219551596191952658585679327927808}\cdot t^{15}-\frac{1335337535407712069995177645993009407403524315341953063631625}{96708852521658439103192383905317171358655855616}\cdot t^{13}+\frac{152791988285748761332482382324727177349994343611564893873375}{3719571250833016888584322457896814283025225216}\cdot t^{11}-\frac{4635584095347505642223792677587578908012764570708037999279125}{59513140013328270217349159326349028528403603456}\cdot t^9+\frac{10556175685090291234201524157913883859275654096455353941608625}{119026280026656540434698318652698057056807206912}\cdot t^7-\frac{13063732950334203429399596854206267330900742447866011205541875}{238052560053313080869396637305396114113614413824}\cdot t^5+\frac{7332115608620337099121646950355075119657811815644263925211875}{476105120106626161738793274610792228227228827648}\cdot t^3-\frac{613534018006080977160851631739772482956498672166138016604375}{476105120106626161738793274610792228227228827648}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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