Rule: Q[3, 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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{43}-\frac{141644373894142665788}{40988561757168329}\cdot t^{41}+\frac{27723802857885632081740}{40988561757168329}\cdot t^{39}-\frac{171668308938568114900110}{2157292724061491}\cdot t^{37}+\frac{27161461233596456941273515}{4314585448122982}\cdot t^{35}-\frac{3063077734441637407449767085}{8629170896245964}\cdot t^{33}+\frac{31833357402938260827767844735}{2157292724061491}\cdot t^{31}-\frac{1991054253294801032959790994825}{4314585448122982}\cdot t^{29}+\frac{379095202259066772119225757647475}{34516683584983856}\cdot t^{27}-\frac{13806249252872268447356943790473525}{69033367169967712}\cdot t^{25}+\frac{192416784264613991730961245490432875}{69033367169967712}\cdot t^{23}-\frac{4088016083931311005286071684846546125}{138066734339935424}\cdot t^{21}+\frac{131265614542177507026601215319459764375}{552266937359741696}\cdot t^{19}-\frac{1571235685468908541266190508111435450625}{1104533874719483392}\cdot t^{17}+\frac{3438428917617006179267323864303131144375}{552266937359741696}\cdot t^{15}-\frac{21426998193666641308217295462349433360625}{1104533874719483392}\cdot t^{13}+\frac{732614764596555335100969631108500999714375}{17672541995511734272}\cdot t^{11}-\frac{2036865469423890662057680038540916200590625}{35345083991023468544}\cdot t^9+\frac{1703506700447161122318105388201387990340625}{35345083991023468544}\cdot t^7-\frac{1514374029519950696534165552373634493784375}{70690167982046937088}\cdot t^5+\frac{1145924863808828573664109359893103314034375}{282760671928187748352}\cdot t^3-\frac{111067956871100921542007595344653162040625}{565521343856375496704}\cdot t$

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.