Rule: Q[4, 30]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{34}-\frac{567773609961636667}{686534065894227}\cdot t^{32}+\frac{784833867605037245286}{2974980952208317}\cdot t^{30}-\frac{135995881961556908108770}{2974980952208317}\cdot t^{28}+\frac{14653092749850591024550590}{2974980952208317}\cdot t^{26}-\frac{80793158921542062391734450}{228844688631409}\cdot t^{24}+\frac{3994692428210336200863562950}{228844688631409}\cdot t^{22}-\frac{138759478635486717629873024850}{228844688631409}\cdot t^{20}+\frac{3406887642967770843226006893000}{228844688631409}\cdot t^{18}-\frac{58903134534490493231598547048500}{228844688631409}\cdot t^{16}+\frac{707787279734315147199966280628250}{228844688631409}\cdot t^{14}-\frac{5773156439684625208411049676570750}{228844688631409}\cdot t^{12}+\frac{30805229026894107650439729046142250}{228844688631409}\cdot t^{10}-\frac{101640901340067736881237691997058750}{228844688631409}\cdot t^8+\frac{189868531146751068406252517170361250}{228844688631409}\cdot t^6-\frac{173027155586036759972837216002023750}{228844688631409}\cdot t^4+\frac{57284128499247205673336055183414375}{228844688631409}\cdot t^2-\frac{2846913802557759570759470087461875}{228844688631409}$

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.