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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{14}-\frac{3816}{7}\cdot t^{12}+\frac{44964}{7}\cdot t^{10}-\frac{225630}{7}\cdot t^8+68715\cdot t^6-\frac{108945}{2}\cdot t^4+\frac{46845}{4}\cdot t^2-\frac{2835}{8}$
• $P_3$:
  $16\cdot t^{32}-\frac{145880276916639796403374251}{52431098359167264314725}\cdot t^{30}+\frac{1690260013507913278170899361837}{8074389147311758704467650}\cdot t^{28}-\frac{145325868536576333709704149190181}{16148778294623517408935300}\cdot t^{26}+\frac{317792788693620937263898185934755}{1291902263569881392714824}\cdot t^{24}-\frac{11637126235344435787790483341866075}{2583804527139762785429648}\cdot t^{22}+\frac{19028882673288851051971116120765393}{335559029498670491614240}\cdot t^{20}-\frac{3664949469168123464050991266713353403}{7382298648970750815513280}\cdot t^{18}+\frac{44616380610825570683052977964784550829}{14764597297941501631026560}\cdot t^{16}-\frac{74804183090863790563102920048120107763}{5905838919176600652410624}\cdot t^{14}+\frac{423410312254280518150564647398840816841}{11811677838353201304821248}\cdot t^{12}-\frac{142488140088505333256723661438683784051}{2147577788791491146331136}\cdot t^{10}+\frac{328454090406804103160453789439733850061}{4295155577582982292662272}\cdot t^8-\frac{62459293157586099964924761942781562619}{1227187307880852083617792}\cdot t^6+\frac{42572530290889973607125231398040112105}{2454374615761704167235584}\cdot t^4-\frac{11917688480399429337305848980747769785}{4908749231523408334471168}\cdot t^2+\frac{659823981998511440734350428572845975}{9817498463046816668942336}$

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.