Rule: Q[5, 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.

• $P_1$:
  $32\cdot t^5-160\cdot t^3+120\cdot t$
• $P_2$:
  $32\cdot t^{39}-\frac{13600341999454669930384}{1197449949929852181}\cdot t^{37}+\frac{32466442949283715584101816}{17961749248947782715}\cdot t^{35}-\frac{613954528574114947481120012}{3592349849789556543}\cdot t^{33}+\frac{414299863116772047766971928}{38627417739672651}\cdot t^{31}-\frac{18262619486258512712656341340}{38627417739672651}\cdot t^{29}+\frac{583744330062853506749123382230}{38627417739672651}\cdot t^{27}-\frac{4591200108704901655376456436393}{12875805913224217}\cdot t^{25}+\frac{322653878303028274445994591215175}{51503223652896868}\cdot t^{23}-\frac{8456502998253147373070886206931075}{103006447305793736}\cdot t^{21}+\frac{164615055228194731251402018715882875}{206012894611587472}\cdot t^{19}-\frac{2356050689539866882034217681216155875}{412025789223174944}\cdot t^{17}+\frac{12193353900640574462472045582290006925}{412025789223174944}\cdot t^{15}-\frac{89074648746832008495787917246175919625}{824051578446349888}\cdot t^{13}+\frac{443509278300380644486025971929909184125}{1648103156892699776}\cdot t^{11}-\frac{1431501981711177354983742283934070808125}{3296206313785399552}\cdot t^9+\frac{11120145374060218342455763230277246670625}{26369650510283196416}\cdot t^7-\frac{11544674399865881289867482768486791567125}{52739301020566392832}\cdot t^5+\frac{5188336940221526480407053246696052693125}{105478602041132785664}\cdot t^3-\frac{624530389960994686840541252268800038125}{210957204082265571328}\cdot t$

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.