Rule: Q[4, 36]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{40}-\frac{341384445679051736881988}{482488103220068946583}\cdot t^{38}+\frac{866827912104624957804625657}{3859904825760551572664}\cdot t^{36}-\frac{81777639157637308804245083715}{1929952412880275786332}\cdot t^{34}+\frac{1863522063074372953669375624785}{350900438705504688424}\cdot t^{32}-\frac{20528305751217575968865263268010}{43862554838188086053}\cdot t^{30}+\frac{2627397971294990805729610244743095}{87725109676376172106}\cdot t^{28}-\frac{62180826700852334918609421822225855}{43862554838188086053}\cdot t^{26}+\frac{4394939367298964202049283983610614125}{87725109676376172106}\cdot t^{24}-\frac{58145470360752004763694113793064974750}{43862554838188086053}\cdot t^{22}+\frac{4595619962901554810261455292564586022125}{175450219352752344212}\cdot t^{20}-\frac{33644557457079201201492672073853471818875}{87725109676376172106}\cdot t^{18}+\frac{720768269075042383798316722614585318441375}{175450219352752344212}\cdot t^{16}-\frac{1385946952337049101149666519378600408023750}{43862554838188086053}\cdot t^{14}+\frac{14920873379056689322130383356950643194641875}{87725109676376172106}\cdot t^{12}-\frac{27134221550208133978108046485752961093329375}{43862554838188086053}\cdot t^{10}+\frac{126916780419505443943935403625320930489674375}{87725109676376172106}\cdot t^8-\frac{88534485253184024610373522740943585631703750}{43862554838188086053}\cdot t^6+\frac{518264281322371435395988771873603714804021875}{350900438705504688424}\cdot t^4-\frac{75931760376274454542746755157859973863115625}{175450219352752344212}\cdot t^2+\frac{7549586918999902539895455536602404155765625}{350900438705504688424}$

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.