Rule: Q[4, 10, 18]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{14}-\frac{477}{7}\cdot t^{12}+\frac{11241}{7}\cdot t^{10}-\frac{112815}{7}\cdot t^8+68715\cdot t^6-108945\cdot t^4+46845\cdot t^2-2835$
• $P_3$:
  $t^{32}-\frac{145880276916639796403374251}{419448786873338114517800}\cdot t^{30}+\frac{1690260013507913278170899361837}{32297556589247034817870600}\cdot t^{28}-\frac{145325868536576333709704149190181}{32297556589247034817870600}\cdot t^{26}+\frac{317792788693620937263898185934755}{1291902263569881392714824}\cdot t^{24}-\frac{11637126235344435787790483341866075}{1291902263569881392714824}\cdot t^{22}+\frac{19028882673288851051971116120765393}{83889757374667622903560}\cdot t^{20}-\frac{3664949469168123464050991266713353403}{922787331121343851939160}\cdot t^{18}+\frac{44616380610825570683052977964784550829}{922787331121343851939160}\cdot t^{16}-\frac{74804183090863790563102920048120107763}{184557466224268770387832}\cdot t^{14}+\frac{423410312254280518150564647398840816841}{184557466224268770387832}\cdot t^{12}-\frac{142488140088505333256723661438683784051}{16777951474933524580712}\cdot t^{10}+\frac{328454090406804103160453789439733850061}{16777951474933524580712}\cdot t^8-\frac{62459293157586099964924761942781562619}{2396850210704789225816}\cdot t^6+\frac{42572530290889973607125231398040112105}{2396850210704789225816}\cdot t^4-\frac{11917688480399429337305848980747769785}{2396850210704789225816}\cdot t^2+\frac{659823981998511440734350428572845975}{2396850210704789225816}$

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.