Rule: Q[4, 27]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{31}-\frac{1733893254976743}{4263259793878}\cdot t^{29}+\frac{3507164896639212966}{49027487629597}\cdot t^{27}-\frac{703432775795215778325}{98054975259194}\cdot t^{25}+\frac{22329286500781131063075}{49027487629597}\cdot t^{23}-\frac{81958994450919132378975}{4263259793878}\cdot t^{21}+\frac{1175944167101498734239300}{2131629896939}\cdot t^{19}-\frac{46137771541636426411434675}{4263259793878}\cdot t^{17}+\frac{307091726299187887869937125}{2131629896939}\cdot t^{15}-\frac{5439345752883001170870784125}{4263259793878}\cdot t^{13}+\frac{15491870316508596139940060250}{2131629896939}\cdot t^{11}-\frac{107806127340207725167962848625}{4263259793878}\cdot t^9+\frac{106195135331703505454470978875}{2131629896939}\cdot t^7-\frac{212700560299676707590815608125}{4263259793878}\cdot t^5+\frac{46882440173786719625278155000}{2131629896939}\cdot t^3-\frac{14114684606831488089300515625}{4263259793878}\cdot t$

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.