Rule: Q[1, 2, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-3\cdot t$
• $P_3$:
  $2\cdot t^9-\frac{117}{4}\cdot t^7+\frac{945}{8}\cdot t^5-\frac{2205}{16}\cdot t^3+\frac{945}{32}\cdot t$
• $P_4$:
  $2\cdot t^{53}-\frac{21387140945855829472998079268690365449394403568032506463415670307351}{17835692609090827687195820508779203504644822889964979983105555100}\cdot t^{51}+\frac{25583416799738950832710544304540211040155121491070006004616244924570569}{77288001306060253311181888871376548520127565856514913260124072100}\cdot t^{49}-\frac{3367734385487531873785904925313610687563941288494301219931894976240876763}{60245006146262351298972549274098642949022512872770599054045430560}\cdot t^{47}+\frac{18249963121032385511805600172461688016712419056479805040221313107720202167055}{2819466287645078040791915306027816490014253602445664035729326150208}\cdot t^{45}-\frac{1710246991080873164445882005960835538855071866505279626322622630903462799412749}{3132740319605642267546572562253129433349170669384071150810362389120}\cdot t^{43}+\frac{217910584324680059688403825649731542683415519680976012837238736302519277443783929}{6265480639211284535093145124506258866698341338768142301620724778240}\cdot t^{41}-\frac{1651248509435287176667071299789526735657203319097765273116036923728965503118795829}{963920098340197620783560788385578287184360205964329584864726888960}\cdot t^{39}+\frac{1344120687891077844440448744398167684712445466673130227212962786107152796356626255}{20293054701898897279653911334433227098618109599249043891888987136}\cdot t^{37}-\frac{82396994660766238957838528636637941668050697911805439302279716706212671951963061879}{40586109403797794559307822668866454197236219198498087783777974272}\cdot t^{35}+\frac{4027441745451077220451790327357744673977259008094282332151570544653894793669247585289}{81172218807595589118615645337732908394472438396996175567555948544}\cdot t^{33}-\frac{78689876251919795701126065722810185399752243430926356333260400571204722091019267500297}{81172218807595589118615645337732908394472438396996175567555948544}\cdot t^{31}+\frac{2458350515653663949720892405553714984165184806103490879164484764197161739866911335497381}{162344437615191178237231290675465816788944876793992351135111897088}\cdot t^{29}-\frac{61254070012419105101847174931111060012999353756941975999142252650457859130013783993026835}{324688875230382356474462581350931633577889753587984702270223794176}\cdot t^{27}+\frac{1211568441495969153917230388098502162867689675379044467632959105529631528456369029151127215}{649377750460764712948925162701863267155779507175969404540447588352}\cdot t^{25}-\frac{18889062005374854056003472173342078562986877763269002621233402265495281824209597010118473675}{1298755500921529425897850325403726534311559014351938809080895176704}\cdot t^{23}+\frac{9995678490668658159150081791791558810062679940498718904769513231963125451261711838352405725}{112935260949698210947639158730758829070570349074081635572251754496}\cdot t^{21}-\frac{46896298486860040823579204043782879503354620767509096055982630596561065279985845992413771025}{112935260949698210947639158730758829070570349074081635572251754496}\cdot t^{19}+\frac{667750327947768950272578831525539029974427334535439232689211021611809570239677382470230326625}{451741043798792843790556634923035316282281396296326542289007017984}\cdot t^{17}-\frac{7069230255910502493059551944651182587513455087352086890307576402100015030375445949096719775375}{1806964175195171375162226539692141265129125585185306169156028071936}\cdot t^{15}+\frac{27108476322713882504337471550424276643478499623731491767756808162543712505273682330280816919875}{3613928350390342750324453079384282530258251170370612338312056143872}\cdot t^{13}-\frac{72789580885123300648053809414523441670913041167511762404932674096295525880110722523034958006125}{7227856700780685500648906158768565060516502340741224676624112287744}\cdot t^{11}+\frac{130651573221769208772288426103446639640838503378659091338860807415628036283949182037618653219625}{14455713401561371001297812317537130121033004681482449353248224575488}\cdot t^9-\frac{146549061453340025332571041723481608957766102213267742411409360158847399217074953267743411735625}{28911426803122742002595624635074260242066009362964898706496449150976}\cdot t^7+\frac{92286468725354381498804525099405365226876050398074235777201454593416121279082721528382175273125}{57822853606245484005191249270148520484132018725929797412992898301952}\cdot t^5-\frac{26843873072432791996538703194732703399998216867299523842605458162179458723497844532914583355625}{115645707212490968010382498540297040968264037451859594825985796603904}\cdot t^3+\frac{2286182671409517585669369075399265517499855929125919277204159158991536848674906872071844296875}{231291414424981936020764997080594081936528074903719189651971593207808}\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.