Rule: Q[4, 10, 20]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{14}-\frac{477}{7}\cdot t^{12}+\frac{11241}{7}\cdot t^{10}-\frac{112815}{7}\cdot t^8+68715\cdot t^6-108945\cdot t^4+46845\cdot t^2-2835$
• $P_3$:
  $t^{34}-\frac{1688006409519343599558860052543}{3642441958493277806607614783}\cdot t^{32}+\frac{336624437237613799793651018080014}{3642441958493277806607614783}\cdot t^{30}-\frac{268069903794378950702890599183782310}{25497093709452944646253303481}\cdot t^{28}+\frac{213661811712597515665803399061644129270}{280468030803982391108786338291}\cdot t^{26}-\frac{801465532123379609245439608446310259130}{21574463907998645469906641407}\cdot t^{24}+\frac{27088153180427119751412883521241051620630}{21574463907998645469906641407}\cdot t^{22}-\frac{1195644098854259433458847765041929288941510}{40066861543426055872683762613}\cdot t^{20}+\frac{20065445200560783376604427345845373377247300}{40066861543426055872683762613}\cdot t^{18}-\frac{236736007146679146492509235640826313106458600}{40066861543426055872683762613}\cdot t^{16}+\frac{1939091720655802763962854669566540067518991150}{40066861543426055872683762613}\cdot t^{14}-\frac{830024167893438157743094796294719681471204050}{3082066272571235067129520201}\cdot t^{12}+\frac{275904163183924589508896060446759870495108650}{280187842961021369739047291}\cdot t^{10}-\frac{630579557455251488763466230565478612215494750}{280187842961021369739047291}\cdot t^8+\frac{119272875381963976684197304263899705128449750}{40026834708717338534149613}\cdot t^6-\frac{81085286179309389378125105695623670720235250}{40026834708717338534149613}\cdot t^4+\frac{22674878655728214539314553393680084053993375}{40026834708717338534149613}\cdot t^2-\frac{1255094291201017792255717299740481308128875}{40026834708717338534149613}$

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.