Rule: Q[4, 49]

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^{53}-\frac{120467144407256828403785304449623849061606}{93327259163492604202079550460405149381}\cdot t^{51}+\frac{1076718766733956729741760849481357034492832773}{1399908887452389063031193256906077240715}\cdot t^{49}-\frac{131194567176661181120967832125057609974609347016}{466636295817463021010397752302025746905}\cdot t^{47}+\frac{1433895292408893970637290030137358993710092919626}{20288534600759261783060771839218510735}\cdot t^{45}-\frac{17558634686228814329288774985579084433579496561372}{1352568973383950785537384789281234049}\cdot t^{43}+\frac{2444410141183355836845008454147088004760548328260754}{1352568973383950785537384789281234049}\cdot t^{41}-\frac{264049752215165516343132962980715930132639680398641256}{1352568973383950785537384789281234049}\cdot t^{39}+\frac{22477533112029903206427642275988625403708835410237449491}{1352568973383950785537384789281234049}\cdot t^{37}-\frac{1523104813132377180735010299510172050779366368779073863858}{1352568973383950785537384789281234049}\cdot t^{35}+\frac{82655323607513830610994298773911001871169798890895230693845}{1352568973383950785537384789281234049}\cdot t^{33}-\frac{3602896318592631786704854406416570185692280103531031879604240}{1352568973383950785537384789281234049}\cdot t^{31}+\frac{126182000975826452987034727434293634505352560257067173245502660}{1352568973383950785537384789281234049}\cdot t^{29}-\frac{3543074797479309639184952833094631358564662579780798637397316360}{1352568973383950785537384789281234049}\cdot t^{27}+\frac{79404697758976140421939469961862928448461993683780200004740264780}{1352568973383950785537384789281234049}\cdot t^{25}-\frac{1410495198326134893290824410406175708163555433925082554481310218000}{1352568973383950785537384789281234049}\cdot t^{23}+\frac{19667629618245547729502461417084662909692641806501983691280709820375}{1352568973383950785537384789281234049}\cdot t^{21}-\frac{212523193858090173838651430481796337407531041487521793288126929035250}{1352568973383950785537384789281234049}\cdot t^{19}+\frac{1750124560558320119063288391842716850775534581480939435399423876339625}{1352568973383950785537384789281234049}\cdot t^{17}-\frac{10747699474791370344319368607424057440185387140545288345843425965217000}{1352568973383950785537384789281234049}\cdot t^{15}+\frac{47843530687095869981662103863293381644713951720308715302181275611463750}{1352568973383950785537384789281234049}\cdot t^{13}-\frac{148653752307266744655167490086512092495493953181180900614682553189377500}{1352568973383950785537384789281234049}\cdot t^{11}+\frac{306069422560052082567309644783305005251067902608982492337793486976741250}{1352568973383950785537384789281234049}\cdot t^9-\frac{387495362748258153911235144302964237279219937176902210265379102840485000}{1352568973383950785537384789281234049}\cdot t^7+\frac{268606742965148712233673923894868265805527640153244406185088255580683125}{1352568973383950785537384789281234049}\cdot t^5-\frac{83130774770622881784398829950061777047950302533936375489379498101568750}{1352568973383950785537384789281234049}\cdot t^3+\frac{7233185736413139754813855578736257141339775088057493766028685415621875}{1352568973383950785537384789281234049}\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.