Rule: Q[4, 5, 32]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^9-21\cdot t^7+108\cdot t^5-135\cdot t^3+45\cdot t$
• $P_3$:
  $t^{41}-\frac{22024992854302650810837451846489608801389437708401}{32438330777928274825188044875952364404415805309}\cdot t^{39}+\frac{46896059474992255072654884544297564031555949687762348}{227068315445497923776316314131666550830910637163}\cdot t^{37}-\frac{1209769863376173427258606939778990587884387771995641731}{32438330777928274825188044875952364404415805309}\cdot t^{35}+\frac{1014372862444109274622251313680311153306611143187869747075}{227068315445497923776316314131666550830910637163}\cdot t^{33}-\frac{85318286003173570763538827410680774845553747903874179134220}{227068315445497923776316314131666550830910637163}\cdot t^{31}+\frac{179447265298064666796911259784885660456229010791022902558160}{7829941911913721509528148763160915545893470247}\cdot t^{29}-\frac{1155026012248219195646387436131074769995616309868070416567420}{1118563130273388787075449823308702220841924321}\cdot t^{27}+\frac{38809884085321226664571048661847381925246458773640581099349330}{1118563130273388787075449823308702220841924321}\cdot t^{25}-\frac{975409792678696727187303211611565884889461901626374259299823750}{1118563130273388787075449823308702220841924321}\cdot t^{23}+\frac{18292811206194013395038217054623739067483022581182177165028203000}{1118563130273388787075449823308702220841924321}\cdot t^{21}-\frac{254105716981407670251184351300267094800885862999343469915366709250}{1118563130273388787075449823308702220841924321}\cdot t^{19}+\frac{2582017269596425634500132840700204585609821023066397268548229618250}{1118563130273388787075449823308702220841924321}\cdot t^{17}-\frac{18843657601795408557529204128404980683007709179408556607776734840500}{1118563130273388787075449823308702220841924321}\cdot t^{15}+\frac{96285874487947109898882634905523051563816045182043297932614224150000}{1118563130273388787075449823308702220841924321}\cdot t^{13}-\frac{332585804207631017632986407103027862899139385144553707894794769287500}{1118563130273388787075449823308702220841924321}\cdot t^{11}+\frac{739562384406692726410916872909189054645134825979516541520518266438125}{1118563130273388787075449823308702220841924321}\cdot t^9-\frac{987702250282296244969953762004619160717977154435061917520298480968125}{1118563130273388787075449823308702220841924321}\cdot t^7+\frac{715891848152658202011762995146369437144768496200493113158869176022500}{1118563130273388787075449823308702220841924321}\cdot t^5-\frac{240680240368651875561966582235537585048972107162411138863287136484375}{1118563130273388787075449823308702220841924321}\cdot t^3+\frac{26802627074204618133600274930228771410752733081173302735020759478125}{1118563130273388787075449823308702220841924321}\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.