Rule: Q[2, 7, 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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^9-\frac{346}{5}\cdot t^7+\frac{1743}{5}\cdot t^5-\frac{1113}{2}\cdot t^3+\frac{399}{2}\cdot t$
• $P_3$:
  $4\cdot t^{25}-\frac{3996542237238873402}{8668431607928285}\cdot t^{23}+\frac{1110940457535288120331}{50276903325984053}\cdot t^{21}-\frac{3193129745837663521251159}{5530459365858245830}\cdot t^{19}+\frac{125410447049968218592107248}{13826148414645614575}\cdot t^{17}-\frac{4933242633342244128706595251}{55304593658582458300}\cdot t^{15}+\frac{12278462268531611687762578533}{22121837463432983320}\cdot t^{13}-\frac{95665691290200967625369237103}{44243674926865966640}\cdot t^{11}+\frac{16445562475294184528223386277}{3217721812862979392}\cdot t^9-\frac{222571687427214277786313843709}{32177218128629793920}\cdot t^7+\frac{312026495095950148930485331899}{64354436257259587840}\cdot t^5-\frac{1300279447112577931849497921}{887647396651856384}\cdot t^3+\frac{3218976882263878499935860507}{25741774502903835136}\cdot t$

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.