Rule: Q[26, 43]

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.

• $P_1$:
  $t^{26}-325\cdot t^{24}+44850\cdot t^{22}-3453450\cdot t^{20}+164038875\cdot t^{18}-5019589575\cdot t^{16}+100391791500\cdot t^{14}-1305093289500\cdot t^{12}+10767019638375\cdot t^{10}-53835098191875\cdot t^8+150738274937250\cdot t^6-205552193096250\cdot t^4+102776096548125\cdot t^2-7905853580625$
• $P_2$:
  $t^{69}-\frac{9521246181320200151638248650514295561705681470331969993}{5456123242652626621680000822168059176059192909996139}\cdot t^{67}+\frac{7805148858705022256579461867250010064230471088747125087930}{5456123242652626621680000822168059176059192909996139}\cdot t^{65}-\frac{12001059850960930731742936147195642121954353105121923490647780}{16368369727957879865040002466504177528177578729988417}\cdot t^{63}+\frac{4317969777298430106331156273166376066739856056267455206364849280}{16368369727957879865040002466504177528177578729988417}\cdot t^{61}-\frac{386983584169138048178086389489255650780752390801236679535951444800}{5456123242652626621680000822168059176059192909996139}\cdot t^{59}+\frac{80810664187746350247369169167604198282380206903342192153668713846500}{5456123242652626621680000822168059176059192909996139}\cdot t^{57}-\frac{13449003712708120770887264436989626450890111267648675674942435056166900}{5456123242652626621680000822168059176059192909996139}\cdot t^{55}+\frac{1816366295743303312386927740621060440068869450071035259989192029613742500}{5456123242652626621680000822168059176059192909996139}\cdot t^{53}-\frac{201676176303146050203385877421656870508365984839187282527976549378156125500}{5456123242652626621680000822168059176059192909996139}\cdot t^{51}+\frac{18584497562750676871584644489740891883231059176914351523420055939903092839700}{5456123242652626621680000822168059176059192909996139}\cdot t^{49}-\frac{1431081020438922162509034724923391630449092177801388077769779139119462525181900}{5456123242652626621680000822168059176059192909996139}\cdot t^{47}+\frac{92531386603084310628740830466577718863052145731602254259592223126319309824400000}{5456123242652626621680000822168059176059192909996139}\cdot t^{45}-\frac{5039766103387320487160281894610755011232763598342550575805810626386594132723844000}{5456123242652626621680000822168059176059192909996139}\cdot t^{43}+\frac{231640960698324270688783432178315555527856596109637610986357269647887656818376566500}{5456123242652626621680000822168059176059192909996139}\cdot t^{41}-\frac{8990127088823542074586195808723141313304029681083265644679768054570465726770545756500}{5456123242652626621680000822168059176059192909996139}\cdot t^{39}+\frac{294470824772110496082964790616101943775715881641937142356190486566215177991206495689250}{5456123242652626621680000822168059176059192909996139}\cdot t^{37}-\frac{8127659119480336040690297750329797460450113991403866507308571382497915851085134428643750}{5456123242652626621680000822168059176059192909996139}\cdot t^{35}+\frac{188538117763454294619200662857340499857898056452686618501333688136188292103492319622215000}{5456123242652626621680000822168059176059192909996139}\cdot t^{33}-\frac{3662136609069552276511473773610895127982150896796231130894315271018894911337665085812402500}{5456123242652626621680000822168059176059192909996139}\cdot t^{31}+\frac{59272902074768357327335332305174664301282628110955305191715040316709718198448758652652440000}{5456123242652626621680000822168059176059192909996139}\cdot t^{29}-\frac{27396099535627022036097686148392256428069155995711085237724589877335505751872330093591320000}{188142180781125055920000028350622730208937686551591}\cdot t^{27}+\frac{301791797704570895797639223920571214731938038279769055485417286650047045569824929184379437500}{188142180781125055920000028350622730208937686551591}\cdot t^{25}-\frac{2706667543691075641753502933322179046843514029912022481697794598091219429486377144337266187500}{188142180781125055920000028350622730208937686551591}\cdot t^{23}+\frac{19537609571452590527930600089236375117323880337636906534153766331489833713815003144099559312500}{188142180781125055920000028350622730208937686551591}\cdot t^{21}-\frac{111909880339473062346401708880090615585836772333764726454709138399803029080648259974841632687500}{188142180781125055920000028350622730208937686551591}\cdot t^{19}+\frac{499804945936989897120987604123015155533355597539736760049529203761300078648892422185394491937500}{188142180781125055920000028350622730208937686551591}\cdot t^{17}-\frac{1702478239193822841017164238748649770839402877090506733910359921154144119330413872101615925312500}{188142180781125055920000028350622730208937686551591}\cdot t^{15}+\frac{4299561689834717806903296610718205063645581888038741996300769082195627585644593011558631395000000}{188142180781125055920000028350622730208937686551591}\cdot t^{13}-\frac{7756271982136547457884960101487343071747804577011682403386771019912984943032064805537648157500000}{188142180781125055920000028350622730208937686551591}\cdot t^{11}+\frac{9499026743016008285880701683653682734530374057690505713542704215658264282856553598098993995937500}{188142180781125055920000028350622730208937686551591}\cdot t^9-\frac{7340619869099020717068320172069253722896878371690991470390523204977790795962542185278293787187500}{188142180781125055920000028350622730208937686551591}\cdot t^7+\frac{3194582858534957773411621037043702409614369591663427391880052078524191540235982727054357077734375}{188142180781125055920000028350622730208937686551591}\cdot t^5-\frac{640072548490537307175118535407861600165787086283020152195539603297666576239776839647306817578125}{188142180781125055920000028350622730208937686551591}\cdot t^3+\frac{37167013185898177933379786171792107450239562923352688136639843392198776912272560925178202343750}{188142180781125055920000028350622730208937686551591}\cdot t$

Warning: This rule has negative weights!

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.