Rule: Q[3, 6, 48]

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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^9-117\cdot t^7+\frac{945}{2}\cdot t^5-\frac{2205}{4}\cdot t^3+\frac{945}{8}\cdot t$
• $P_3$:
  $8\cdot t^{57}-\frac{3445309416318978752482380285423175684680230898320616164332576236328329645492111}{521610878054816017116131796902692833611616799045958849818696817688311456723}\cdot t^{55}+\frac{10138760996665475777651974223260404601490204267670064776108445962791803415841737595}{4078048682974016133817030412148325790054458610722951007673447847381344116198}\cdot t^{53}-\frac{357479866206088125745663792919257043314431330569546126710975509937786248439744777452375}{628019497177998484607822683470842171668386626051334455181710968496726993894492}\cdot t^{51}+\frac{111946466668427568121412449480891470409706597999696155717245105422848644050111110555466835}{1256038994355996969215645366941684343336773252102668910363421936993453987788984}\cdot t^{49}-\frac{1823804120383677035056697190782731423430317015601519103320404834670435105254721508009948315}{179434142050856709887949338134526334762396178871809844337631705284779141112712}\cdot t^{47}+\frac{13690226780967820671252072484509533909940914059536638990299030803867615390604356981156567465}{15602968873987539990256464185610985631512711206244334290228843937806881835888}\cdot t^{45}-\frac{3879040525920347242250180595693778102862846616561422402987326022155797665919381606475242525}{65974498410095306512712322137890002670244022013718115392088135043580895712}\cdot t^{43}+\frac{37318840334008495138083660444329567644825959283179961894744600548731877482090187401462521425}{11995363347290055729584058570525455030953458547948748253106933644287435584}\cdot t^{41}-\frac{614217772231924154354635817928893928205081501550844362487238648149283194388354157945940388425}{4670760949387278337183173248700177180194267045218981620678806020784488192}\cdot t^{39}+\frac{4723052119204925559916560298715766712978877245521589260516401642797076082807943474146229557522525}{1055591974561524904203397154206240042723904352219489846273410160697294331392}\cdot t^{37}-\frac{259905904477336457223734050958910161414424160952104348292291193819579381780099052120639529135975325}{2111183949123049808406794308412480085447808704438979692546820321394588662784}\cdot t^{35}+\frac{11590483233134510706189489927067585274695267015328999029863833982540095553623321875463810526650693625}{4222367898246099616813588616824960170895617408877959385093640642789177325568}\cdot t^{33}-\frac{9519413233061789005007757218405494075999127924766172964329668781700322477534928907038696908307327125}{191925813556640891673344937128407280495255336767179972049710938308598969344}\cdot t^{31}+\frac{3060295541777628487054375696514166696075238602423304580432264960449387820967054293523677251337459722875}{4222367898246099616813588616824960170895617408877959385093640642789177325568}\cdot t^{29}-\frac{72046243981629632179879462179736839387467951132267620361071698083627466559162158318968663124356924370375}{8444735796492199233627177233649920341791234817755918770187281285578354651136}\cdot t^{27}+\frac{339565221757632824225744768141168344272916442565321888954771377709294969353528554414673296737988466391375}{4222367898246099616813588616824960170895617408877959385093640642789177325568}\cdot t^{25}-\frac{81370256598334771320115887069734274724131886384110392177344562127511467133990725224201422988490563971528125}{135115772743875187738034835738398725468659757084094700322996500569253674418176}\cdot t^{23}+\frac{87108522121628032042632011912088495513693402484805314822727579399705351230869931138544956625429977365571875}{24566504135250034134188151952436131903392683106199036422363000103500668076032}\cdot t^{21}-\frac{796080139399540441096243672245198471916858669213432748244213493767515166787477785634040380944350830430896875}{49133008270500068268376303904872263806785366212398072844726000207001336152064}\cdot t^{19}+\frac{5555135932996416622110180432032978034262679536175837055235649623261634529330212606342221145042876592507834375}{98266016541000136536752607809744527613570732424796145689452000414002672304128}\cdot t^{17}-\frac{14501049703044417580049649939951398961796555624298392738504706443139743053752837710396784648529762641416884375}{98266016541000136536752607809744527613570732424796145689452000414002672304128}\cdot t^{15}+\frac{55195926366374273905353696895509207345343285459499023451942899771036009543465043247666184559171720587062046875}{196532033082000273073505215619489055227141464849592291378904000828005344608256}\cdot t^{13}-\frac{148089609018298518626019153469185370195172927395691946651279118535695813934209931031835385331408875748143859375}{393064066164000546147010431238978110454282929699184582757808001656010689216512}\cdot t^{11}+\frac{267380197561656994923117264725803663445939142974133950566425544976420729208585318127201344893965706210178328125}{786128132328001092294020862477956220908565859398369165515616003312021378433024}\cdot t^9-\frac{606790859032922964504297423217200773294476802486215954803695492565021651804712387835769592573555574500435078125}{3144512529312004369176083449911824883634263437593476662062464013248085513732096}\cdot t^7+\frac{387098726435022551935484127224463974876460085979683037957358341987519057862951686310376837785100789712292890625}{6289025058624008738352166899823649767268526875186953324124928026496171027464192}\cdot t^5-\frac{112908884982232061108478784068197790842846807991973388337287591228719701506063245957714964756079563013541640625}{12578050117248017476704333799647299534537053750373906648249856052992342054928384}\cdot t^3+\frac{9280949664014822815275080621085192296701322762874262974406334052744228269010467911047446515113602805835078125}{25156100234496034953408667599294599069074107500747813296499712105984684109856768}\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.