Rule: Q[2, 3, 4, 24]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^9-\frac{142}{3}\cdot t^7+\frac{1399}{9}\cdot t^5-\frac{2965}{18}\cdot t^3+\frac{295}{6}\cdot t$
• $P_4$:
  $4\cdot t^{33}-\frac{55228743238444850054839965670281091790733211659266}{63182519542706008820545556987124360511709738529}\cdot t^{31}+\frac{79119328926466581326024603194966773667069687784151007}{947737793140590132308183354806865407675646077935}\cdot t^{29}-\frac{8728445323345597808774140034898917207923223062417069429}{1895475586281180264616366709613730815351292155870}\cdot t^{27}+\frac{68824339226732729335379092422906046985908141630553946573}{421216796951373392136970379914162403411398256860}\cdot t^{25}-\frac{662652947579923606478401819707486712947341870037008133855}{168486718780549356854788151965664961364559302744}\cdot t^{23}+\frac{454060196471565716921218623827113497118909337137050216135}{6877008929818341096113802121047549443451400112}\cdot t^{21}-\frac{75401507282798797245389025505980062418103463107926570376035}{96278125017456775345593229694665692208319601568}\cdot t^{19}+\frac{1267274454439789951824494544368244661134284220011865762100845}{192556250034913550691186459389331384416639203136}\cdot t^{17}-\frac{2143152701684930850243636579529532963913761881878808777536705}{55016071438546728768910416968380395547611200896}\cdot t^{15}+\frac{123301210512180682745375842388068255610914139813300760103739175}{770225000139654202764745837557325537666556812544}\cdot t^{13}-\frac{686388472182978158320047396885397376264801351242077212677422525}{1540450000279308405529491675114651075333113625088}\cdot t^{11}+\frac{2487879770623122924450370460500087200056392599124616175535775925}{3080900000558616811058983350229302150666227250176}\cdot t^9-\frac{787431751846006787000850141789215588517281665393234723598867925}{880257143016747660302566671494086328761779214336}\cdot t^7+\frac{958912810758155454685458845297971376371982748508452052413420525}{1760514286033495320605133342988172657523558428672}\cdot t^5-\frac{526768892923732411179482267280038984784449260418646917353278375}{3521028572066990641210266685976345315047116857344}\cdot t^3+\frac{41144959956984255291896461630401263429453382571132069953885375}{3521028572066990641210266685976345315047116857344}\cdot t$

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.