Rule: Q[7, 40]

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.

• $P_1$:
  $t^7-21\cdot t^5+105\cdot t^3-105\cdot t$
• $P_2$:
  $t^{47}-\frac{29489850349848120765366333948308786701}{30229520413264054439634042230102181}\cdot t^{45}+\frac{4374565959746955679221300719564444926465}{10076506804421351479878014076700727}\cdot t^{43}-\frac{20043160977742038095258341406173758391941805}{171300615675162975157926239303912359}\cdot t^{41}+\frac{3662968541530098150486838626595366910225478025}{171300615675162975157926239303912359}\cdot t^{39}-\frac{481653659978986061803553836561684777603426424505}{171300615675162975157926239303912359}\cdot t^{37}+\frac{47192752650206445411960224360827302413260671351255}{171300615675162975157926239303912359}\cdot t^{35}-\frac{207122810427720357384657829975682284471027497934275}{10076506804421351479878014076700727}\cdot t^{33}+\frac{11925999482010571412929395396337813370174087557374150}{10076506804421351479878014076700727}\cdot t^{31}-\frac{17224708219845454378860666730030991020100062169270250}{325048606594237144512194002474217}\cdot t^{29}+\frac{601564544008296335748093410752195380275894979819948150}{325048606594237144512194002474217}\cdot t^{27}-\frac{16378276125387518102897999018929246872912472676793225150}{325048606594237144512194002474217}\cdot t^{25}+\frac{346237531748327637497973711232414883446047728410245828750}{325048606594237144512194002474217}\cdot t^{23}-\frac{5641458772927257730296603734605613873404243181123347428750}{325048606594237144512194002474217}\cdot t^{21}+\frac{70069505626252901878222757426001048007411440129655914431250}{325048606594237144512194002474217}\cdot t^{19}-\frac{653399166594965081451676413635169510681757693883388210416250}{325048606594237144512194002474217}\cdot t^{17}+\frac{4482461486906210681369193956276739006145013661027011303938125}{325048606594237144512194002474217}\cdot t^{15}-\frac{22022629004975606999276595757477413491850117269849694717103125}{325048606594237144512194002474217}\cdot t^{13}+\frac{74762968223193501667439366939426243898821887981854138786946875}{325048606594237144512194002474217}\cdot t^{11}-\frac{167032862720640462540482307669067523742848279352080548936359375}{325048606594237144512194002474217}\cdot t^9+\frac{229185226256258907389982777205890464948959796456746133861446875}{325048606594237144512194002474217}\cdot t^7-\frac{173755859918439226628844803263684297895697102090236708301196875}{325048606594237144512194002474217}\cdot t^5+\frac{60451945614242210330039493030950543969613413108851433618953125}{325048606594237144512194002474217}\cdot t^3-\frac{6256346681180566489229743524278615609711128802947346644265625}{325048606594237144512194002474217}\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.