Rule: Q[1, 12, 22]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{13}-78\cdot t^{11}+2145\cdot t^9-25740\cdot t^7+135135\cdot t^5-270270\cdot t^3+135135\cdot t$
• $P_3$:
  $t^{35}-\frac{104183722427}{223695465}\cdot t^{33}+\frac{49747981712374}{521956085}\cdot t^{31}-\frac{1183349601145470}{104391217}\cdot t^{29}+\frac{91193242189830462}{104391217}\cdot t^{27}-\frac{4807731238765183278}{104391217}\cdot t^{25}+\frac{178520343673970119734}{104391217}\cdot t^{23}-\frac{4737442080901430349702}{104391217}\cdot t^{21}+\frac{12895216245629117959680}{14913031}\cdot t^{19}-\frac{175818765562104382892460}{14913031}\cdot t^{17}+\frac{1696563534341565839526390}{14913031}\cdot t^{15}-\frac{11363377682679217847408790}{14913031}\cdot t^{13}+\frac{51269666800511609160552270}{14913031}\cdot t^{11}-\frac{148989298097147016195665550}{14913031}\cdot t^9+\frac{260405409094543658973520350}{14913031}\cdot t^7-\frac{34965086608775141668728450}{2130433}\cdot t^5+\frac{14344888314278558359612575}{2130433}\cdot t^3-\frac{1557077815890323403759225}{2130433}\cdot t$

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.