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.

• $P_1$:
  $t^3-3\cdot t$
• $P_2$:
  $t^9-\frac{117}{4}\cdot t^7+\frac{945}{4}\cdot t^5-\frac{2205}{4}\cdot t^3+\frac{945}{4}\cdot t$
• $P_3$:
  $t^{53}-\frac{21387140945855829472998079268690365449394403568032506463415670307351}{17835692609090827687195820508779203504644822889964979983105555100}\cdot t^{51}+\frac{25583416799738950832710544304540211040155121491070006004616244924570569}{38644000653030126655590944435688274260063782928257456630062036050}\cdot t^{49}-\frac{3367734385487531873785904925313610687563941288494301219931894976240876763}{15061251536565587824743137318524660737255628218192649763511357640}\cdot t^{47}+\frac{18249963121032385511805600172461688016712419056479805040221313107720202167055}{352433285955634755098989413253477061251781700305708004466165768776}\cdot t^{45}-\frac{1710246991080873164445882005960835538855071866505279626322622630903462799412749}{195796269975352641721660785140820589584323166836504446925647649320}\cdot t^{43}+\frac{217910584324680059688403825649731542683415519680976012837238736302519277443783929}{195796269975352641721660785140820589584323166836504446925647649320}\cdot t^{41}-\frac{1651248509435287176667071299789526735657203319097765273116036923728965503118795829}{15061251536565587824743137318524660737255628218192649763511357640}\cdot t^{39}+\frac{1344120687891077844440448744398167684712445466673130227212962786107152796356626255}{158539489858585134997296182300259586707953981244133155405382712}\cdot t^{37}-\frac{82396994660766238957838528636637941668050697911805439302279716706212671951963061879}{158539489858585134997296182300259586707953981244133155405382712}\cdot t^{35}+\frac{4027441745451077220451790327357744673977259008094282332151570544653894793669247585289}{158539489858585134997296182300259586707953981244133155405382712}\cdot t^{33}-\frac{78689876251919795701126065722810185399752243430926356333260400571204722091019267500297}{79269744929292567498648091150129793353976990622066577702691356}\cdot t^{31}+\frac{2458350515653663949720892405553714984165184806103490879164484764197161739866911335497381}{79269744929292567498648091150129793353976990622066577702691356}\cdot t^{29}-\frac{61254070012419105101847174931111060012999353756941975999142252650457859130013783993026835}{79269744929292567498648091150129793353976990622066577702691356}\cdot t^{27}+\frac{1211568441495969153917230388098502162867689675379044467632959105529631528456369029151127215}{79269744929292567498648091150129793353976990622066577702691356}\cdot t^{25}-\frac{18889062005374854056003472173342078562986877763269002621233402265495281824209597010118473675}{79269744929292567498648091150129793353976990622066577702691356}\cdot t^{23}+\frac{9995678490668658159150081791791558810062679940498718904769513231963125451261711838352405725}{3446510649099676847767308310875208406694651766176807726203972}\cdot t^{21}-\frac{46896298486860040823579204043782879503354620767509096055982630596561065279985845992413771025}{1723255324549838423883654155437604203347325883088403863101986}\cdot t^{19}+\frac{667750327947768950272578831525539029974427334535439232689211021611809570239677382470230326625}{3446510649099676847767308310875208406694651766176807726203972}\cdot t^{17}-\frac{7069230255910502493059551944651182587513455087352086890307576402100015030375445949096719775375}{6893021298199353695534616621750416813389303532353615452407944}\cdot t^{15}+\frac{27108476322713882504337471550424276643478499623731491767756808162543712505273682330280816919875}{6893021298199353695534616621750416813389303532353615452407944}\cdot t^{13}-\frac{72789580885123300648053809414523441670913041167511762404932674096295525880110722523034958006125}{6893021298199353695534616621750416813389303532353615452407944}\cdot t^{11}+\frac{130651573221769208772288426103446639640838503378659091338860807415628036283949182037618653219625}{6893021298199353695534616621750416813389303532353615452407944}\cdot t^9-\frac{146549061453340025332571041723481608957766102213267742411409360158847399217074953267743411735625}{6893021298199353695534616621750416813389303532353615452407944}\cdot t^7+\frac{92286468725354381498804525099405365226876050398074235777201454593416121279082721528382175273125}{6893021298199353695534616621750416813389303532353615452407944}\cdot t^5-\frac{26843873072432791996538703194732703399998216867299523842605458162179458723497844532914583355625}{6893021298199353695534616621750416813389303532353615452407944}\cdot t^3+\frac{2286182671409517585669369075399265517499855929125919277204159158991536848674906872071844296875}{6893021298199353695534616621750416813389303532353615452407944}\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.