Rule: Q[10, 20]

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.

• $P_1$:
  $1024\cdot t^{10}-23040\cdot t^8+161280\cdot t^6-403200\cdot t^4+302400\cdot t^2-30240$
• $P_2$:
  $1024\cdot t^{30}-\frac{15801325217280}{90446489}\cdot t^{28}+\frac{15000076105102080}{1175804357}\cdot t^{26}-\frac{617480697697603200}{1175804357}\cdot t^{24}+\frac{1921096776460392000}{142130197}\cdot t^{22}-\frac{421573787180200896480}{1847692561}\cdot t^{20}+\frac{4765643597559987543600}{1847692561}\cdot t^{18}-\frac{36219180067063843228200}{1847692561}\cdot t^{16}+\frac{183302574867543432487500}{1847692561}\cdot t^{14}-\frac{46435083211026270002250}{142130197}\cdot t^{12}+\frac{8693651240836419512475}{12920927}\cdot t^{10}-\frac{20999445685393754305125}{25841854}\cdot t^8+\frac{26771564505690036293625}{51683708}\cdot t^6-\frac{15034567253335707616875}{103367416}\cdot t^4+\frac{2726884722974218419375}{206734832}\cdot t^2-\frac{99673906355990591625}{413469664}$

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.