Rule: Q[3, 6, 44]

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^{53}-\frac{21387140945855829472998079268690365449394403568032506463415670307351}{4458923152272706921798955127194800876161205722491244995776388775}\cdot t^{51}+\frac{25583416799738950832710544304540211040155121491070006004616244924570569}{19322000326515063327795472217844137130031891464128728315031018025}\cdot t^{49}-\frac{3367734385487531873785904925313610687563941288494301219931894976240876763}{15061251536565587824743137318524660737255628218192649763511357640}\cdot t^{47}+\frac{18249963121032385511805600172461688016712419056479805040221313107720202167055}{704866571911269510197978826506954122503563400611416008932331537552}\cdot t^{45}-\frac{1710246991080873164445882005960835538855071866505279626322622630903462799412749}{783185079901410566886643140563282358337292667346017787702590597280}\cdot t^{43}+\frac{217910584324680059688403825649731542683415519680976012837238736302519277443783929}{1566370159802821133773286281126564716674585334692035575405181194560}\cdot t^{41}-\frac{1651248509435287176667071299789526735657203319097765273116036923728965503118795829}{240980024585049405195890197096394571796090051491082396216181722240}\cdot t^{39}+\frac{1344120687891077844440448744398167684712445466673130227212962786107152796356626255}{5073263675474724319913477833608306774654527399812260972972246784}\cdot t^{37}-\frac{82396994660766238957838528636637941668050697911805439302279716706212671951963061879}{10146527350949448639826955667216613549309054799624521945944493568}\cdot t^{35}+\frac{4027441745451077220451790327357744673977259008094282332151570544653894793669247585289}{20293054701898897279653911334433227098618109599249043891888987136}\cdot t^{33}-\frac{78689876251919795701126065722810185399752243430926356333260400571204722091019267500297}{20293054701898897279653911334433227098618109599249043891888987136}\cdot t^{31}+\frac{2458350515653663949720892405553714984165184806103490879164484764197161739866911335497381}{40586109403797794559307822668866454197236219198498087783777974272}\cdot t^{29}-\frac{61254070012419105101847174931111060012999353756941975999142252650457859130013783993026835}{81172218807595589118615645337732908394472438396996175567555948544}\cdot t^{27}+\frac{1211568441495969153917230388098502162867689675379044467632959105529631528456369029151127215}{162344437615191178237231290675465816788944876793992351135111897088}\cdot t^{25}-\frac{18889062005374854056003472173342078562986877763269002621233402265495281824209597010118473675}{324688875230382356474462581350931633577889753587984702270223794176}\cdot t^{23}+\frac{9995678490668658159150081791791558810062679940498718904769513231963125451261711838352405725}{28233815237424552736909789682689707267642587268520408893062938624}\cdot t^{21}-\frac{46896298486860040823579204043782879503354620767509096055982630596561065279985845992413771025}{28233815237424552736909789682689707267642587268520408893062938624}\cdot t^{19}+\frac{667750327947768950272578831525539029974427334535439232689211021611809570239677382470230326625}{112935260949698210947639158730758829070570349074081635572251754496}\cdot t^{17}-\frac{7069230255910502493059551944651182587513455087352086890307576402100015030375445949096719775375}{451741043798792843790556634923035316282281396296326542289007017984}\cdot t^{15}+\frac{27108476322713882504337471550424276643478499623731491767756808162543712505273682330280816919875}{903482087597585687581113269846070632564562792592653084578014035968}\cdot t^{13}-\frac{72789580885123300648053809414523441670913041167511762404932674096295525880110722523034958006125}{1806964175195171375162226539692141265129125585185306169156028071936}\cdot t^{11}+\frac{130651573221769208772288426103446639640838503378659091338860807415628036283949182037618653219625}{3613928350390342750324453079384282530258251170370612338312056143872}\cdot t^9-\frac{146549061453340025332571041723481608957766102213267742411409360158847399217074953267743411735625}{7227856700780685500648906158768565060516502340741224676624112287744}\cdot t^7+\frac{92286468725354381498804525099405365226876050398074235777201454593416121279082721528382175273125}{14455713401561371001297812317537130121033004681482449353248224575488}\cdot t^5-\frac{26843873072432791996538703194732703399998216867299523842605458162179458723497844532914583355625}{28911426803122742002595624635074260242066009362964898706496449150976}\cdot t^3+\frac{2286182671409517585669369075399265517499855929125919277204159158991536848674906872071844296875}{57822853606245484005191249270148520484132018725929797412992898301952}\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.