Rule: Q[5, 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.

• $P_1$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_2$:
  $t^{13}-\frac{170}{3}\cdot t^{11}+\frac{3251}{3}\cdot t^9-8652\cdot t^7+29631\cdot t^5-41790\cdot t^3+19215\cdot t$
• $P_3$:
  $t^{29}-\frac{42089393394686530251326}{139527960992289822237}\cdot t^{27}+\frac{895873287982445463318218581}{23022113563727820669105}\cdot t^{25}-\frac{195347741650439324822853990556}{69066340691183462007315}\cdot t^{23}+\frac{8876737578247005811868386501051}{69066340691183462007315}\cdot t^{21}-\frac{88217550694764034042247326662266}{23022113563727820669105}\cdot t^{19}+\frac{352601232147804563918755868779777}{4604422712745564133821}\cdot t^{17}-\frac{23723960538896647700251983599610392}{23022113563727820669105}\cdot t^{15}+\frac{14202892543910658710228117364411877}{1534807570915188044607}\cdot t^{13}-\frac{7566461182199792723609235514300354}{139527960992289822237}\cdot t^{11}+\frac{27837716764475429834380073083743739}{139527960992289822237}\cdot t^9-\frac{876099666373540673457118398434580}{2022144362207098873}\cdot t^7+\frac{23393352488929388152056163419837621}{46509320330763274079}\cdot t^5-\frac{12223121550963078278390259709418010}{46509320330763274079}\cdot t^3+\frac{1939616588277833633824116159509265}{46509320330763274079}\cdot t$

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.