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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{11}-\frac{6923}{82}\cdot t^9+\frac{97479}{164}\cdot t^7-\frac{566685}{328}\cdot t^5+\frac{1313235}{656}\cdot t^3-\frac{418635}{656}\cdot t$
• $P_4$:
  $4\cdot t^{29}-\frac{1739343849360700900915385139711369413654620871}{2804684868715267961056838243178129357542014}\cdot t^{27}+\frac{5982798057179293696423447768778308948230504277893}{145843613173193933974955588645262726592184728}\cdot t^{25}-\frac{444894871727392010877813490812968980067212146130725}{291687226346387867949911177290525453184369456}\cdot t^{23}+\frac{20636133589143136862923244626466638346274168399450075}{583374452692775735899822354581050906368738912}\cdot t^{21}-\frac{89557860086548338875531185093871077501902695367899625}{166678415055078781685663529880300258962496832}\cdot t^{19}+\frac{28473520591687962022667037361972728427519766653631325}{5208700470471211927676985308759383092578026}\cdot t^{17}-\frac{12496074056386778434148502163077088684565735481491842575}{333356830110157563371327059760600517924993664}\cdot t^{15}+\frac{114783998837346305536354759434197630639156865161531801625}{666713660220315126742654119521201035849987328}\cdot t^{13}-\frac{26652344991611305307564030982019675575470296695880693875}{51285666170793471287896470732400079680768256}\cdot t^{11}+\frac{408530383267663189575183041312491241299789284010629351375}{410285329366347770303171765859200637446146048}\cdot t^9-\frac{937072754814471899185380815570135204223847727610488686875}{820570658732695540606343531718401274892292096}\cdot t^7+\frac{1165100165932814596183175323376924581360967312898482998125}{1641141317465391081212687063436802549784584192}\cdot t^5-\frac{655318829248406657027461674460666195426726751865358063125}{3282282634930782162425374126873605099569168384}\cdot t^3+\frac{54750150401706830323145649752298333950458786514292650625}{3282282634930782162425374126873605099569168384}\cdot t$

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.