Rule: Q[1, 12, 26]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{13}-78\cdot t^{11}+2145\cdot t^9-25740\cdot t^7+135135\cdot t^5-270270\cdot t^3+135135\cdot t$
• $P_3$:
  $t^{39}-\frac{998308440773553}{1727893965901}\cdot t^{37}+\frac{257797121629388445}{1727893965901}\cdot t^{35}-\frac{670600399023694791405}{29374197420317}\cdot t^{33}+\frac{957335975157389397570}{413721090427}\cdot t^{31}-\frac{4833290940455632562068590}{29374197420317}\cdot t^{29}+\frac{1743983194628973421245455190}{205619381942219}\cdot t^{27}-\frac{66407769738530164501070406750}{205619381942219}\cdot t^{25}+\frac{1886275941158732992361667603000}{205619381942219}\cdot t^{23}-\frac{40081393642039013752801121952000}{205619381942219}\cdot t^{21}+\frac{4775691777988514452177397503500}{1546010390543}\cdot t^{19}-\frac{3290540115190505881160881066500}{90941787679}\cdot t^{17}+\frac{28057244555319864163368451683750}{90941787679}\cdot t^{15}-\frac{170198127402598137979760926623750}{90941787679}\cdot t^{13}+\frac{710631850751208144414730604351250}{90941787679}\cdot t^{11}-\frac{1947383105495281531721738296166250}{90941787679}\cdot t^9+\frac{3263757841954301373168344757095625}{90941787679}\cdot t^7-\frac{2992249040222128651171112083303125}{90941787679}\cdot t^5+\frac{1230875600141909941353488131903125}{90941787679}\cdot t^3-\frac{144526707157778177345428818628125}{90941787679}\cdot t$

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.