Rule: Q[2, 3, 4, 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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^9-\frac{71}{3}\cdot t^7+\frac{1399}{9}\cdot t^5-\frac{2965}{9}\cdot t^3+\frac{590}{3}\cdot t$
• $P_4$:
  $t^{25}-\frac{174007375964576309435136638373}{733464270055645672977186689}\cdot t^{23}+\frac{153951172651106060050334095501747}{6601178430500811056794680201}\cdot t^{21}-\frac{24632777273882457889865235837261211}{19803535291502433170384040603}\cdot t^{19}+\frac{2354053015318629102743582121494602924}{59410605874507299511152121809}\cdot t^{17}-\frac{46538604634608219310868929659510737410}{59410605874507299511152121809}\cdot t^{15}+\frac{14767899455653971947839679012960762410}{1523348868577110243875695431}\cdot t^{13}-\frac{113035766929709626151596261583095747070}{1523348868577110243875695431}\cdot t^{11}+\frac{518594847574714663638285824411403957695}{1523348868577110243875695431}\cdot t^9-\frac{149887996532323417856644169086966276615}{169260985397456693763966159}\cdot t^7+\frac{200323274179145436469215778597849666625}{169260985397456693763966159}\cdot t^5-\frac{112297857423043112018826691186454021075}{169260985397456693763966159}\cdot t^3+\frac{5095223509927489689014550324111477250}{56420328465818897921322053}\cdot t$

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.