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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{40}-\frac{2731075565432413895055904}{482488103220068946583}\cdot t^{38}+\frac{866827912104624957804625657}{964976206440137893166}\cdot t^{36}-\frac{81777639157637308804245083715}{964976206440137893166}\cdot t^{34}+\frac{1863522063074372953669375624785}{350900438705504688424}\cdot t^{32}-\frac{10264152875608787984432631634005}{43862554838188086053}\cdot t^{30}+\frac{2627397971294990805729610244743095}{350900438705504688424}\cdot t^{28}-\frac{62180826700852334918609421822225855}{350900438705504688424}\cdot t^{26}+\frac{4394939367298964202049283983610614125}{1403601754822018753696}\cdot t^{24}-\frac{29072735180376002381847056896532487375}{701800877411009376848}\cdot t^{22}+\frac{4595619962901554810261455292564586022125}{11228814038576150029568}\cdot t^{20}-\frac{33644557457079201201492672073853471818875}{11228814038576150029568}\cdot t^{18}+\frac{720768269075042383798316722614585318441375}{44915256154304600118272}\cdot t^{16}-\frac{692973476168524550574833259689300204011875}{11228814038576150029568}\cdot t^{14}+\frac{14920873379056689322130383356950643194641875}{89830512308609200236544}\cdot t^{12}-\frac{27134221550208133978108046485752961093329375}{89830512308609200236544}\cdot t^{10}+\frac{126916780419505443943935403625320930489674375}{359322049234436800946176}\cdot t^8-\frac{44267242626592012305186761370471792815851875}{179661024617218400473088}\cdot t^6+\frac{518264281322371435395988771873603714804021875}{5749152787750988815138816}\cdot t^4-\frac{75931760376274454542746755157859973863115625}{5749152787750988815138816}\cdot t^2+\frac{7549586918999902539895455536602404155765625}{22996611151003955260555264}$

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.