Rule: Q[2, 3, 4, 14]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^9-\frac{142}{3}\cdot t^7+\frac{1399}{9}\cdot t^5-\frac{2965}{18}\cdot t^3+\frac{295}{6}\cdot t$
• $P_4$:
  $4\cdot t^{23}-\frac{169625390220735424001363}{463875841537913130667}\cdot t^{21}+\frac{62890330448819181324966253}{4638758415379131306670}\cdot t^{19}-\frac{133315719513259180037270755649}{500985908860946181120360}\cdot t^{17}+\frac{3039062481038901597402449119997}{1001971817721892362240720}\cdot t^{15}-\frac{2774845170323086267554658180579}{133596242362918981632096}\cdot t^{13}+\frac{2082238692711273394162593945307}{24290225884167087569472}\cdot t^{11}-\frac{10149207587812731381384163286473}{48580451768334175138944}\cdot t^9+\frac{3096125185255355834767730775959}{10795655948518705586432}\cdot t^7-\frac{4374253038620181155772559235737}{21591311897037411172864}\cdot t^5+\frac{2660648657524539749820890878195}{43182623794074822345728}\cdot t^3-\frac{230060587953399507869373472755}{43182623794074822345728}\cdot t$

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.