Rule: Q[9, 58]

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.

• $P_1$:
  $t^9-36\cdot t^7+378\cdot t^5-1260\cdot t^3+945\cdot t$
• $P_2$:
  $t^{67}-\frac{159992029095990350663250281826508274967843460903963078946587060507669308331}{80545807267577901110367590493415042986939548252710578174568683910362457}\cdot t^{65}+\frac{1938579341564266827881783214979045713770385328416981084156954589313533483224766}{1047095494478512714434778676414395558830214127285237516269392890834711941}\cdot t^{63}-\frac{19179138638977519510737184882641196370212177278590280825168934408754084310953999214}{17800623406134716145391237499044724500113640163849037776579679144190102997}\cdot t^{61}+\frac{15045426801058978093092441347763663655840258913474400280003726187671956090089620417398}{34231968088720607971906225959701393269449308007401995724191690661904044225}\cdot t^{59}-\frac{59518591528113216975905044063201761986303711115455486234191219860386867739352943611187214}{445015585153367903634780937476118112502841004096225944414491978604752574925}\cdot t^{57}+\frac{1079986485901372379361826295079645845442639975083177734386244368966362671261802242851401694}{34231968088720607971906225959701393269449308007401995724191690661904044225}\cdot t^{55}-\frac{9938951614825148348903238454699039630640786539690421824999882683181687691097023357741447526}{1679304094918369447678418631985351367935249072061229978922611240017934245}\cdot t^{53}+\frac{6830312713530081675100288185453554192701580564963942695254312488655296779453016792682565842}{7598661062979047274562980235227834244050900778557601714581951312298345}\cdot t^{51}-\frac{170128736798315520797915155114775753521519644223561872942811492586175459099986222683938972642}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{49}+\frac{17534891662642353523502367188689294456780720280553342607776309260507674292253958676991332352582}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{47}-\frac{1505596309071763051033586550844950665015524083590049345038864852742066804338675093700521255566806}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{45}+\frac{108185530048438058956060591135504083944044759934622066508154217537957424850257955661899127023435430}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{43}-\frac{6524382471691696127662671318260247139757436755798319151031828518756517261377981878643762062407972310}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{41}+\frac{330720360708096906401258709527075572485374779851409668508871850525980636873274338629491406141873256670}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{39}-\frac{14093881639043518855016359704207921945262984119597036788612175785454203052660074972048997591795338652270}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{37}+\frac{504473793490675972323938214473645984763436084877398465640033559930118828579712583456176233813997339617860}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{35}-\frac{15134986902454182746348717624780903479275904890058234718079583498267371887058116729784041551918809404138400}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{33}+\frac{379364731724640102705908046736043712790447204394150994879178089919603555829203639983380887004965376640733050}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{31}-\frac{7909120173103459434569003667529110856141110362931019174516847441296286442462501032831549034011754539971747050}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{29}+\frac{136356304287310651400391549266473660656088736727315607233689271289060701255701093724173509842760058370615679050}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{27}-\frac{1929786388641014195247420659740061717478982082472321873175170956027161601507491568958264379462374817871251294650}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{25}+\frac{22215355783041576870217148580634240121065697396526169879479705070347530997666895879026825316577760094232380421250}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{23}-\frac{205671189617676568861553504893479142763985501985338190597362387984908514054035474877333485910528754932845419211250}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{21}+\frac{1509877202083136356571816043666560117049429344685925679375771014559676117190656530104123531698211683625379959983750}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{19}-\frac{8635705951666215086279591777480127518141126400862967635967290911038712357223791199482491190880467354519904428858750}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{17}+\frac{37632225373158978299683964092852376474348363110414011654779703332875669387350860230610149811098669172948006440601250}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{15}-\frac{121418593197323739495745608103022582732111605094563845613780915946911263452228895150116313213713959224440308166231250}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{13}+\frac{279321660575445047945956086406558455169859073517063039895846249469406517656714675829093492379158421082994028695681250}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^{11}-\frac{435263689502834850923807091982698941415197053073727764368985164595482653324354682867694758883535783757712695781411250}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^9+\frac{426988858407740557804602987356290170815784979795505993993774612370283664526559893181624891346993959213377604722086250}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^7-\frac{235521878580832637040234685551242901051143597678885793193999769341164735947553509256714430955229531832771780741796250}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^5+\frac{59897740528174559560832543399233058057765411662829108881423374709862493895964390193593666536437979748546764952784375}{1519732212595809454912596047045566848810180155711520342916390262459669}\cdot t^3-\frac{4464425723434047487702298507287448612585382405413535463955986295294091642949553143121494999269309299041090616990625}{1519732212595809454912596047045566848810180155711520342916390262459669}\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.