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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^{39}-\frac{42915193612261847582544878238169649}{62958174504496216169015452340832}\cdot t^{37}+\frac{39340257054363348447395763418558876661}{188874523513488648507046357022496}\cdot t^{35}-\frac{3570921378093460968383983741100202952285}{94437261756744324253523178511248}\cdot t^{33}+\frac{35865924641690410601790239642531362277665}{7869771813062027021126931542604}\cdot t^{31}-\frac{6076811986370637275092424936467957709945335}{15739543626124054042253863085208}\cdot t^{29}+\frac{373747031723820140570255406700654936170877045}{15739543626124054042253863085208}\cdot t^{27}-\frac{1416773013178170637001175069798738818763897105}{1311628635510337836854488590434}\cdot t^{25}+\frac{96251371789290534307622641963877676883464458625}{2623257271020675673708977180868}\cdot t^{23}-\frac{425870316780935994041361777291287158950428526375}{456218655829682725862430814064}\cdot t^{21}+\frac{8093559647569396962767066281927055438251951613625}{456218655829682725862430814064}\cdot t^{19}-\frac{56994739075220990836206258099426335082563031762375}{228109327914841362931215407032}\cdot t^{17}+\frac{293367708855621824760224984260177343607382755523875}{114054663957420681465607703516}\cdot t^{15}-\frac{4324014302290064541449472337155420056446552834966875}{228109327914841362931215407032}\cdot t^{13}+\frac{22130846018478748548288483515771569061577613877525625}{228109327914841362931215407032}\cdot t^{11}-\frac{9406293128516292234509094852066879951052844064800625}{28513665989355170366401925879}\cdot t^9+\frac{79475809402824538918916129246686620338666559061708125}{114054663957420681465607703516}\cdot t^7-\frac{748561094051731693139081998104963914846207735664148125}{912437311659365451724861628128}\cdot t^5+\frac{403370034899718385409712554880660963805900293390496875}{912437311659365451724861628128}\cdot t^3-\frac{31487846715248591251022549917788619806813814078284375}{456218655829682725862430814064}\cdot t$

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.