Rule: Q[2, 3, 6, 18]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^{11}-\frac{6923}{164}\cdot t^9+\frac{97479}{164}\cdot t^7-\frac{566685}{164}\cdot t^5+\frac{1313235}{164}\cdot t^3-\frac{418635}{82}\cdot t$
• $P_4$:
  $t^{29}-\frac{1739343849360700900915385139711369413654620871}{5609369737430535922113676486356258715084028}\cdot t^{27}+\frac{5982798057179293696423447768778308948230504277893}{145843613173193933974955588645262726592184728}\cdot t^{25}-\frac{444894871727392010877813490812968980067212146130725}{145843613173193933974955588645262726592184728}\cdot t^{23}+\frac{20636133589143136862923244626466638346274168399450075}{145843613173193933974955588645262726592184728}\cdot t^{21}-\frac{89557860086548338875531185093871077501902695367899625}{20834801881884847710707941235037532370312104}\cdot t^{19}+\frac{227788164733503696181336298895781827420158133229050600}{2604350235235605963838492654379691546289013}\cdot t^{17}-\frac{12496074056386778434148502163077088684565735481491842575}{10417400940942423855353970617518766185156052}\cdot t^{15}+\frac{114783998837346305536354759434197630639156865161531801625}{10417400940942423855353970617518766185156052}\cdot t^{13}-\frac{26652344991611305307564030982019675575470296695880693875}{400669266959323994436691177596875622506002}\cdot t^{11}+\frac{408530383267663189575183041312491241299789284010629351375}{1602677067837295977746764710387502490024008}\cdot t^9-\frac{937072754814471899185380815570135204223847727610488686875}{1602677067837295977746764710387502490024008}\cdot t^7+\frac{1165100165932814596183175323376924581360967312898482998125}{1602677067837295977746764710387502490024008}\cdot t^5-\frac{655318829248406657027461674460666195426726751865358063125}{1602677067837295977746764710387502490024008}\cdot t^3+\frac{54750150401706830323145649752298333950458786514292650625}{801338533918647988873382355193751245012004}\cdot t$

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.