Rule: Q[1, 26, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^{27}-351\cdot t^{25}+52650\cdot t^{23}-4440150\cdot t^{21}+233107875\cdot t^{19}-7972289325\cdot t^{17}+180705224700\cdot t^{15}-2710578370500\cdot t^{13}+26428139112375\cdot t^{11}-161505294575625\cdot t^9+581419060472250\cdot t^7-1109981842719750\cdot t^5+924984868933125\cdot t^3-213458046676875\cdot t$
• $P_3$:
  $t^{71}-\frac{4123964009500291191467339877579250750572776110737902471}{2240758616243123085684006629009389718779104141555315}\cdot t^{69}+\frac{34514262837776522421562868222626572476723230787851278255509}{21660666623683523161612064080424100614864673368368045}\cdot t^{67}-\frac{18710719957878528493623522133643707173833469137439908003111421}{21660666623683523161612064080424100614864673368368045}\cdot t^{65}+\frac{12838209301807615934473375915717648658379516107588801631523733008}{38989199922630341690901715344763381106756412063062481}\cdot t^{63}-\frac{407044923925804776417985041172795281241751399267136971128366053808}{4332133324736704632322412816084820122972934673673609}\cdot t^{61}+\frac{90384633668591656742320829471237080852973550660468715915996397821440}{4332133324736704632322412816084820122972934673673609}\cdot t^{59}-\frac{16028582397140446373687793616773406029952216747120516722543644271680480}{4332133324736704632322412816084820122972934673673609}\cdot t^{57}+\frac{2311916470748906146748325099809539984484902576856328388483248659429609460}{4332133324736704632322412816084820122972934673673609}\cdot t^{55}-\frac{274829207072733725614722796939341817591141541685617786365695523874036655300}{4332133324736704632322412816084820122972934673673609}\cdot t^{53}+\frac{27187950100296078161249906112792334065754802875380155885335254473325168279300}{4332133324736704632322412816084820122972934673673609}\cdot t^{51}-\frac{2254233106087730440945742337822937991373960067923366992368998084134662885357380}{4332133324736704632322412816084820122972934673673609}\cdot t^{49}+\frac{157453244771730433843976954963786225401783322038613087840535883418036233009943040}{4332133324736704632322412816084820122972934673673609}\cdot t^{47}-\frac{9297426481741861778842199683555269079121393316199958638071094740712071456385976160}{4332133324736704632322412816084820122972934673673609}\cdot t^{45}+\frac{465136465982543801443204286991112241894160394371057667760749084381842690865928890800}{4332133324736704632322412816084820122972934673673609}\cdot t^{43}-\frac{19735519169719483597586902347738266588255208739080662086749242150244272176296676285200}{4332133324736704632322412816084820122972934673673609}\cdot t^{41}+\frac{7979308925396850156564933492479818939423108858249673213321870674551797184310042905150}{48675655334120276767667559731290113741268928917681}\cdot t^{39}-\frac{21650085208211454017648540651770639051305810694751606654350953236676335414267230400810550}{4332133324736704632322412816084820122972934673673609}\cdot t^{37}+\frac{558085886563640018492183961980901012262705839073958491029344648997280769506019190802843950}{4332133324736704632322412816084820122972934673673609}\cdot t^{35}-\frac{12128112375119393737605047137574470187275254466887182724563640575331624399735997959223506750}{4332133324736704632322412816084820122972934673673609}\cdot t^{33}+\frac{221310385758720526754558933750039943225971705027055619465963410037543648264245307516966122000}{4332133324736704632322412816084820122972934673673609}\cdot t^{31}-\frac{116334174610393105298593454470369854042654895180321660087706430007570143911024700400234254000}{149383907749541539045600441933959314585273609437021}\cdot t^{29}+\frac{1472101988820776017968337966727388311096356114553461352388335118175401266231959797750829932000}{149383907749541539045600441933959314585273609437021}\cdot t^{27}-\frac{15342527934682164393236066871107409603590663129191995055731284026977603195365911910555688768000}{149383907749541539045600441933959314585273609437021}\cdot t^{25}+\frac{130447974532112432627352129312910736533617070654296092590531260339671243872072180117528017112500}{149383907749541539045600441933959314585273609437021}\cdot t^{23}-\frac{894334712279164654497106010300332537842975358030007534846373093111653948663883442349718079762500}{149383907749541539045600441933959314585273609437021}\cdot t^{21}+\frac{4873985380719908048108809849010843369194298687727522536169860366324692908051910551159536826262500}{149383907749541539045600441933959314585273609437021}\cdot t^{19}-\frac{20745200878386462060239564073386225314902326576427237767077255099881565400746082998136510288662500}{149383907749541539045600441933959314585273609437021}\cdot t^{17}+\frac{67448403248926258458950443543574760909157150763463276732512597213308934807832621126983071551900000}{149383907749541539045600441933959314585273609437021}\cdot t^{15}-\frac{162823102363085784062261081149164667225076625647560258014779597528582801291801184210064849194000000}{149383907749541539045600441933959314585273609437021}\cdot t^{13}+\frac{281129482361872152330769821872370603455148317094298814224819080950518819088113913841708759234750000}{149383907749541539045600441933959314585273609437021}\cdot t^{11}-\frac{329782524860073298907026655626025396261929597637207706019901821517251721139773398520900051885250000}{149383907749541539045600441933959314585273609437021}\cdot t^9+\frac{243734256325537179260809527851432366121649351663547109413691906594921650236014583162728743806453125}{149383907749541539045600441933959314585273609437021}\cdot t^7-\frac{100273154854445507169319688790360148108481168327445002320009670519331115914909285988167113044640625}{149383907749541539045600441933959314585273609437021}\cdot t^5+\frac{201833253874725784362905665900184266125232413344988491373312343815555575094758059701198079453125}{1678470873590354371298881370044486680733411341989}\cdot t^3-\frac{698702956871074888834996210496515643563832302762889908059187431739722314206534208591870404453125}{149383907749541539045600441933959314585273609437021}\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.