Rule: Q[2, 5, 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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^7-\frac{106}{3}\cdot t^5+\frac{215}{3}\cdot t^3-\frac{55}{2}\cdot t$
• $P_3$:
  $4\cdot t^{25}-\frac{2485846480284814814}{3917479702543341}\cdot t^{23}+\frac{32172829350933064699091}{795248379616298223}\cdot t^{21}-\frac{727510583935616176487947}{530165586410865482}\cdot t^{19}+\frac{14548556139364493604290931}{530165586410865482}\cdot t^{17}-\frac{32533326815945525412952593}{96393742983793724}\cdot t^{15}+\frac{781460072458071965705337975}{302951763663351704}\cdot t^{13}-\frac{7327676586560574966719136165}{605903527326703408}\cdot t^{11}+\frac{7396791576953884479287819685}{220328555391528512}\cdot t^9-\frac{22826622339241546445089698735}{440657110783057024}\cdot t^7+\frac{35276920329102940997326533105}{881314221566114048}\cdot t^5-\frac{22803484244302509213359763675}{1762628443132228096}\cdot t^3+\frac{1038885630882372447020428725}{881314221566114048}\cdot t$

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.