Rule: Q[9, 18]

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.

• $P_1$:
  $512\cdot t^9-9216\cdot t^7+48384\cdot t^5-80640\cdot t^3+30240\cdot t$
• $P_2$:
  $512\cdot t^{27}-\frac{182952532224}{2285023}\cdot t^{25}+\frac{12050044579584}{2285023}\cdot t^{23}-\frac{4835665709184384}{25135253}\cdot t^{21}+\frac{540686374322566752}{125676265}\cdot t^{19}-\frac{7750749833055318096}{125676265}\cdot t^{17}+\frac{72415996849066810464}{125676265}\cdot t^{15}-\frac{6770129571064632528}{1933481}\cdot t^{13}+\frac{2388412457986847418}{175771}\cdot t^{11}-\frac{5707020368910312459}{175771}\cdot t^9+\frac{7892925949480246227}{175771}\cdot t^7-\frac{11372441683416633981}{351542}\cdot t^5+\frac{14009296299489055215}{1406168}\cdot t^3-\frac{2310749345160580905}{2812336}\cdot t$

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.