Rule: Q[3, 72]

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.

• $P_1$:
  $t^3-3\cdot t$
• $P_2$:
  $t^{75}-\frac{1549585851360162397792751389413207139831779}{570831318897806310999477864496173894245}\cdot t^{73}+\frac{1990860837711490739286404540172284684197659462}{570831318897806310999477864496173894245}\cdot t^{71}-\frac{46045058846078898079664165526849559417533884526}{16309466254223037457127938985604968407}\cdot t^{69}+\frac{26376710168596200240781127943133135637761634386707}{16309466254223037457127938985604968407}\cdot t^{67}-\frac{11385762647858263452316504324268853868231151239620213}{16309466254223037457127938985604968407}\cdot t^{65}+\frac{3850684607176606214828659208989201521247290687858711408}{16309466254223037457127938985604968407}\cdot t^{63}-\frac{1047451047503695026766339540372690902720671255929093964304}{16309466254223037457127938985604968407}\cdot t^{61}+\frac{233453349247170495357466773178804010406803448775057703221260}{16309466254223037457127938985604968407}\cdot t^{59}-\frac{732418429995361316324651990935921591963483009437079966792380}{276431631427509109442846423484829973}\cdot t^{57}+\frac{113730687115007785424995669619993229736204989688929583890207720}{276431631427509109442846423484829973}\cdot t^{55}-\frac{14926598028372047143217879000692805408330142294679662685847464920}{276431631427509109442846423484829973}\cdot t^{53}+\frac{1665032036849038633674710842208502598127638161025464989258355930660}{276431631427509109442846423484829973}\cdot t^{51}-\frac{158491627702771243347240379880211250259872334761165354585935820429500}{276431631427509109442846423484829973}\cdot t^{49}+\frac{12909291058178489061831650650603903254468548620965987235854916280334000}{276431631427509109442846423484829973}\cdot t^{47}-\frac{901214233723963558051814216797529097837570308858373703073134183986786000}{276431631427509109442846423484829973}\cdot t^{45}+\frac{53961118933540335271071950121320095757817258851758787922218801709820419750}{276431631427509109442846423484829973}\cdot t^{43}-\frac{2770595603607977301475421747482273527294245524890814692882885028486410914250}{276431631427509109442846423484829973}\cdot t^{41}+\frac{121856716676670361144826216120827149791275156028047717427087257124665059742500}{276431631427509109442846423484829973}\cdot t^{39}-\frac{4582399045036781830341778886064345050226685954298374521624213655113017935597500}{276431631427509109442846423484829973}\cdot t^{37}+\frac{146932458451457871881976666935767160911168239422646172517614408602724481423208750}{276431631427509109442846423484829973}\cdot t^{35}-\frac{4002679146590409083051209414025096230077322036069433414845704237221921525078921250}{276431631427509109442846423484829973}\cdot t^{33}+\frac{92214527289348283106713918356882949624117054923933406600616005536799585836006270000}{276431631427509109442846423484829973}\cdot t^{31}-\frac{1786504830571519040104019435277437792294171615509703966473688080948998722069785650000}{276431631427509109442846423484829973}\cdot t^{29}+\frac{28905042769560918886351714359865029256066830239438122184297650207447656382963212112500}{276431631427509109442846423484829973}\cdot t^{27}-\frac{387340838660229115113650483152265771462567892723712681857912361718933504754812206387500}{276431631427509109442846423484829973}\cdot t^{25}+\frac{4256017809644110719956802654138767678884124871758239941326373629138099006455625939025000}{276431631427509109442846423484829973}\cdot t^{23}-\frac{37881767306789929906874108328479566281183253212423948881872112835432731507179442149575000}{276431631427509109442846423484829973}\cdot t^{21}+\frac{269123035757415611895036327289107876785058911365571815129311545817063459098449031528812500}{276431631427509109442846423484829973}\cdot t^{19}-\frac{1498507298554415660777116551779305176030090532485925735628398757172180167369377042276687500}{276431631427509109442846423484829973}\cdot t^{17}+\frac{6392529024623877312619460382758237294266694341989935712631655272474171672892086703729250000}{276431631427509109442846423484829973}\cdot t^{15}-\frac{20294891001906851003876748442976792516312345753373737080436445122761880375468217279336750000}{276431631427509109442846423484829973}\cdot t^{13}+\frac{46160564691080621234268724733312303597623263510501833704170757996081640619735996632389078125}{276431631427509109442846423484829973}\cdot t^{11}-\frac{71420554275022155244313125228114459061225307078591972124629468342385329707113689410658046875}{276431631427509109442846423484829973}\cdot t^9+\frac{69783706656963467751012398012514789310318420559662116785972830614318979462588995283059843750}{276431631427509109442846423484829973}\cdot t^7-\frac{38367389978342086204827715705392090827603674292253757852226322731432095305881626949371406250}{276431631427509109442846423484829973}\cdot t^5+\frac{9684598878473914377513331278687585574726748957975068231352485303964667481724960202474140625}{276431631427509109442846423484829973}\cdot t^3-\frac{706345088888966155704240304080146966451101761377629130934945303088142129786893840280234375}{276431631427509109442846423484829973}\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.