Rule: Q[2, 3, 34]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{39}-\frac{42915193612261847582544878238169649}{31479087252248108084507726170416}\cdot t^{37}+\frac{39340257054363348447395763418558876661}{188874523513488648507046357022496}\cdot t^{35}-\frac{3570921378093460968383983741100202952285}{188874523513488648507046357022496}\cdot t^{33}+\frac{35865924641690410601790239642531362277665}{31479087252248108084507726170416}\cdot t^{31}-\frac{6076811986370637275092424936467957709945335}{125916349008992432338030904681664}\cdot t^{29}+\frac{373747031723820140570255406700654936170877045}{251832698017984864676061809363328}\cdot t^{27}-\frac{1416773013178170637001175069798738818763897105}{41972116336330810779343634893888}\cdot t^{25}+\frac{96251371789290534307622641963877676883464458625}{167888465345323243117374539575552}\cdot t^{23}-\frac{425870316780935994041361777291287158950428526375}{58395987946199388910391144200192}\cdot t^{21}+\frac{8093559647569396962767066281927055438251951613625}{116791975892398777820782288400384}\cdot t^{19}-\frac{56994739075220990836206258099426335082563031762375}{116791975892398777820782288400384}\cdot t^{17}+\frac{293367708855621824760224984260177343607382755523875}{116791975892398777820782288400384}\cdot t^{15}-\frac{4324014302290064541449472337155420056446552834966875}{467167903569595111283129153601536}\cdot t^{13}+\frac{22130846018478748548288483515771569061577613877525625}{934335807139190222566258307203072}\cdot t^{11}-\frac{9406293128516292234509094852066879951052844064800625}{233583951784797555641564576800768}\cdot t^9+\frac{79475809402824538918916129246686620338666559061708125}{1868671614278380445132516614406144}\cdot t^7-\frac{748561094051731693139081998104963914846207735664148125}{29898745828454087122120265830498304}\cdot t^5+\frac{403370034899718385409712554880660963805900293390496875}{59797491656908174244240531660996608}\cdot t^3-\frac{31487846715248591251022549917788619806813814078284375}{59797491656908174244240531660996608}\cdot t$

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.