Rule: Q[8, 16]

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.

• $P_1$:
  $t^8-28\cdot t^6+210\cdot t^4-420\cdot t^2+105$
• $P_2$:
  $t^{24}-\frac{42379148}{205799}\cdot t^{22}+\frac{17887751826}{1028995}\cdot t^{20}-\frac{808842426868}{1028995}\cdot t^{18}+\frac{4300571720081}{205799}\cdot t^{16}-\frac{69530951380632}{205799}\cdot t^{14}+\frac{684646567527468}{205799}\cdot t^{12}-\frac{364218257071032}{18709}\cdot t^{10}+\frac{1200200825947851}{18709}\cdot t^8-\frac{2018245163718420}{18709}\cdot t^6+\frac{1439457643268190}{18709}\cdot t^4-\frac{291209545596060}{18709}\cdot t^2+\frac{4752962138925}{18709}$

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.