Rule: Q[10, 21]

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.

• $P_1$:
  $1024\cdot t^{10}-23040\cdot t^8+161280\cdot t^6-403200\cdot t^4+302400\cdot t^2-30240$
• $P_2$:
  $1024\cdot t^{31}-\frac{9781470720}{55417}\cdot t^{29}+\frac{725034827520}{55417}\cdot t^{27}-\frac{2774160628479360}{5042947}\cdot t^{25}+\frac{73543973335128000}{5042947}\cdot t^{23}-\frac{2032532345856610080}{7924631}\cdot t^{21}+\frac{24321748604342936400}{7924631}\cdot t^{19}-\frac{200079533048623320600}{7924631}\cdot t^{17}+\frac{1131280660582006238100}{7924631}\cdot t^{15}-\frac{4355476337984380764750}{7924631}\cdot t^{13}+\frac{861410447564587098975}{609587}\cdot t^{11}-\frac{260064800171087659875}{110834}\cdot t^9+\frac{527154492894880323375}{221668}\cdot t^7-\frac{590725613789628526125}{443336}\cdot t^5+\frac{302310908444829335625}{886672}\cdot t^3-\frac{44538274723888425375}{1773344}\cdot t$

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.