Rule: Q[4, 10, 21]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{14}-\frac{3816}{7}\cdot t^{12}+\frac{44964}{7}\cdot t^{10}-\frac{225630}{7}\cdot t^8+68715\cdot t^6-\frac{108945}{2}\cdot t^4+\frac{46845}{4}\cdot t^2-\frac{2835}{8}$
• $P_3$:
  $16\cdot t^{35}-\frac{116820468175793942682357308626008}{34192744932325195010790009931}\cdot t^{33}+\frac{141722944911994376696193675558778296}{444505684120227535140270129103}\cdot t^{31}-\frac{53479779632140244311013931167634513420}{3111539788841592745981890903721}\cdot t^{29}+\frac{1855295758756521871633264433905809458370}{3111539788841592745981890903721}\cdot t^{27}-\frac{480624090698277014569852300194427931771145}{34226937677257520205800799940931}\cdot t^{25}+\frac{15805908728028188132314610572410440858792895}{68453875354515040411601599881862}\cdot t^{23}-\frac{52549419573237496242827846913817338160055955}{19558250101290011546171885680532}\cdot t^{21}+\frac{434194796800440830637313968957225751810119825}{19558250101290011546171885680532}\cdot t^{19}-\frac{2535229806824603357909859868550942437411280325}{19558250101290011546171885680532}\cdot t^{17}+\frac{82642650028528546492484680280861643087664453575}{156466000810320092369375085444256}\cdot t^{15}-\frac{460221022314894088938736092940530016683281804325}{312932001620640184738750170888512}\cdot t^{13}+\frac{130544127632101591038815150298375795089326975575}{48143384864713874575192333982848}\cdot t^{11}-\frac{27675574331726927458049125721964067037628417375}{8753342702675249922762242542336}\cdot t^9+\frac{5437644698085811796633181654396790136260294875}{2500955057907214263646355012096}\cdot t^7-\frac{3916001089920969060598481660191370453394047625}{5001910115814428527292710024192}\cdot t^5+\frac{2299898045864887188776939493575407290648603375}{20007640463257714109170840096768}\cdot t^3-\frac{128915419102045609903091065023757731672658875}{40015280926515428218341680193536}\cdot t$

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.