Rule: Q[1, 2, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-3\cdot t$
• $P_3$:
  $t^{43}-\frac{35411093473535666447}{40988561757168329}\cdot t^{41}+\frac{13861901428942816040870}{40988561757168329}\cdot t^{39}-\frac{171668308938568114900110}{2157292724061491}\cdot t^{37}+\frac{27161461233596456941273515}{2157292724061491}\cdot t^{35}-\frac{3063077734441637407449767085}{2157292724061491}\cdot t^{33}+\frac{254666859223506086622142757880}{2157292724061491}\cdot t^{31}-\frac{15928434026358408263678327958600}{2157292724061491}\cdot t^{29}+\frac{758190404518133544238451515294950}{2157292724061491}\cdot t^{27}-\frac{27612498505744536894713887580947050}{2157292724061491}\cdot t^{25}+\frac{769667137058455966923844981961731500}{2157292724061491}\cdot t^{23}-\frac{16352064335725244021144286739386184500}{2157292724061491}\cdot t^{21}+\frac{262531229084355014053202430638919528750}{2157292724061491}\cdot t^{19}-\frac{3142471370937817082532381016222870901250}{2157292724061491}\cdot t^{17}+\frac{27507431340936049434138590914425049155000}{2157292724061491}\cdot t^{15}-\frac{171415985549333130465738363698795466885000}{2157292724061491}\cdot t^{13}+\frac{732614764596555335100969631108500999714375}{2157292724061491}\cdot t^{11}-\frac{2036865469423890662057680038540916200590625}{2157292724061491}\cdot t^9+\frac{3407013400894322244636210776402775980681250}{2157292724061491}\cdot t^7-\frac{3028748059039901393068331104747268987568750}{2157292724061491}\cdot t^5+\frac{1145924863808828573664109359893103314034375}{2157292724061491}\cdot t^3-\frac{111067956871100921542007595344653162040625}{2157292724061491}\cdot t$

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.