Rule: Q[1, 6, 48]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-21\cdot t^5+105\cdot t^3-105\cdot t$
• $P_3$:
  $t^{55}-\frac{2157887202291549839598462728271433947220487509}{1615127349649056470704171123998417232551497}\cdot t^{53}+\frac{57317307725481531923445798116803252436490128173527}{69450476034909428240279358331931940999714371}\cdot t^{51}-\frac{152308754294474760926816315087646600500881547434417449}{486153332244365997681955508323523586998000597}\cdot t^{49}+\frac{5691301771779020314244191543778009260550336652367946682}{69450476034909428240279358331931940999714371}\cdot t^{47}-\frac{1090150118992252540991844380212441827771058450225219920546}{69450476034909428240279358331931940999714371}\cdot t^{45}+\frac{335428195260988445559848886739337165969947344118292342010}{146829759059005133700379193090765202959227}\cdot t^{43}-\frac{37987017815014518529817171979319713922414733018223693830970}{146829759059005133700379193090765202959227}\cdot t^{41}+\frac{3401256947424589564712579595210154528511138306186304341317305}{146829759059005133700379193090765202959227}\cdot t^{39}-\frac{243335479756895606875675302759914753613684028593568094639815605}{146829759059005133700379193090765202959227}\cdot t^{37}+\frac{14004071357262982928026364296475476713478705242200617882516018365}{146829759059005133700379193090765202959227}\cdot t^{35}-\frac{650750997918782833785399969114275505938198198966323108016387152725}{146829759059005133700379193090765202959227}\cdot t^{33}+\frac{24448440970905391235047073663263592646739901800907294513300205932700}{146829759059005133700379193090765202959227}\cdot t^{31}-\frac{741984029302978902312840750696198270622657599134739825266579732532300}{146829759059005133700379193090765202959227}\cdot t^{29}+\frac{18138775253234927174312726847068748733794205586748598351217026094118300}{146829759059005133700379193090765202959227}\cdot t^{27}-\frac{355465345950691438775086716650907128425128573061932496765053522092535900}{146829759059005133700379193090765202959227}\cdot t^{25}+\frac{5545908369408775327809699973810117367618099597740158759967720352572168125}{146829759059005133700379193090765202959227}\cdot t^{23}-\frac{68258110217397409377018541993995568092274350006431321902265121520987145625}{146829759059005133700379193090765202959227}\cdot t^{21}+\frac{654942959944134779821228699739232281947843838786789515223243796807275885625}{146829759059005133700379193090765202959227}\cdot t^{19}-\frac{4825522778307851960200220554702524780465736402114003295115725826518826110625}{146829759059005133700379193090765202959227}\cdot t^{17}+\frac{26773505126036636714549904556807615420645389827772708006624810891187794416250}{146829759059005133700379193090765202959227}\cdot t^{15}-\frac{109032185241443153435380831539093388212638999676268035371052072676096935881250}{146829759059005133700379193090765202959227}\cdot t^{13}+\frac{314773039306709937673767991644350172894661395975897504795701173412656891106250}{146829759059005133700379193090765202959227}\cdot t^{11}-\frac{613298516797805280845676119777814551046394151120068219571427537633203572706250}{146829759059005133700379193090765202959227}\cdot t^9+\frac{749302015084157301415412441382313005114728210635485450062046019860356416659375}{146829759059005133700379193090765202959227}\cdot t^7-\frac{510069226386900258436188119031190319211909472400547200018085529766016509821875}{146829759059005133700379193090765202959227}\cdot t^5+\frac{156305546526520048008250012199374274085189841817616721753332490990047469546875}{146829759059005133700379193090765202959227}\cdot t^3-\frac{13250468592817984083713901914994696499211439223242558191223105000570755671875}{146829759059005133700379193090765202959227}\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.