Rule: Q[1, 20, 36]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{21}-210\cdot t^{19}+\frac{17955}{2}\cdot t^{17}-203490\cdot t^{15}+\frac{10683225}{4}\cdot t^{13}-\frac{83329155}{4}\cdot t^{11}+\frac{1527701175}{16}\cdot t^9-\frac{1964187225}{8}\cdot t^7+\frac{41247931725}{128}\cdot t^5-\frac{22915517625}{128}\cdot t^3+\frac{13749310575}{512}\cdot t$
• $P_3$:
  $2\cdot t^{57}-\frac{411287889662130948830614956}{343303287907604831431525}\cdot t^{55}+\frac{456602185512307029270930226443}{1373213151630419325726100}\cdot t^{53}-\frac{359183344222952161495206411922161}{6316780497499928898340060}\cdot t^{51}+\frac{1868078708065313720227478277168698187}{277938341889996871526962640}\cdot t^{49}-\frac{8114996755969081899609595907911103235}{13896917094499843576348132}\cdot t^{47}+\frac{21519984755444280436122050814165857761137}{555876683779993743053925280}\cdot t^{45}-\frac{1115709361634285024621507857406221095488859}{555876683779993743053925280}\cdot t^{43}+\frac{4599254899163083383691354793638396646552619}{55587668377999374305392528}\cdot t^{41}-\frac{304930730255493129499045051358575499851550481}{111175336755998748610785056}\cdot t^{39}+\frac{262092661436349985122502190520982956603125770869}{3557610776191959955545121792}\cdot t^{37}-\frac{5730417550047815127907866494260172246061470177649}{3557610776191959955545121792}\cdot t^{35}+\frac{408864614088280072764891076945267146007627719727497}{14230443104767839822180487168}\cdot t^{33}-\frac{67625206156539050832245544410471083698737228417685}{161709580735998179797505536}\cdot t^{31}+\frac{6414133549509081266460555997131196373239187685927285}{1293676645887985438380044288}\cdot t^{29}-\frac{61722773002411177107512300687484784208785734274736235}{1293676645887985438380044288}\cdot t^{27}+\frac{3835438843651576555253050390252851716824483050217829175}{10349413167103883507040354304}\cdot t^{25}-\frac{518802697476515358365933314234849636697823757431010575}{224987242763127902326964224}\cdot t^{23}+\frac{40962236383265312658053651905993701356725724914310677125}{3599795884210046437231427584}\cdot t^{21}-\frac{158258156591001580942901529339480693717945331526737981125}{3599795884210046437231427584}\cdot t^{19}+\frac{1883554064605383073125954233400323381683561353087006199125}{14399183536840185748925710336}\cdot t^{17}-\frac{1056483990271503229011710852118124498673172333102853138875}{3599795884210046437231427584}\cdot t^{15}+\frac{13911046884005759060345008389438453321085391957338317647625}{28798367073680371497851420672}\cdot t^{13}-\frac{16194514034912312179016122792061167994098073571257210596875}{28798367073680371497851420672}\cdot t^{11}+\frac{25363922436958705080585678234558530636767013032373218753125}{57596734147360742995702841344}\cdot t^9-\frac{3107600435397868832710666745003711675122961586633086225625}{14399183536840185748925710336}\cdot t^7+\frac{54584908442380668654488506443791846519411910125964612309375}{921547746357771887931245461504}\cdot t^5-\frac{6931255637463360129590431469199120113045897370906599596875}{921547746357771887931245461504}\cdot t^3+\frac{1067583015073643668378398532684940793829042330432387321875}{3686190985431087551724981846016}\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.