Rule: Q[1, 4, 56]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^5-10\cdot t^3+\frac{15}{2}\cdot t$
• $P_3$:
  $2\cdot t^{61}-\frac{1488698946934398188033760927573771790176396393566}{869747000783558979970315732869543405757899861}\cdot t^{59}+\frac{15451323782868840253307478774649100978278280505809309}{22613422020372533479228209054608128549705396386}\cdot t^{57}-\frac{637764541794905109587346243185576843305970796426316315}{3768903670062088913204701509101354758284232731}\cdot t^{55}+\frac{1843875909873810047181407122422860823642772935906228635}{63210124445485767936347195121196725505815224}\cdot t^{53}-\frac{18101850990628666941810309864986501435770194895611774475}{4862317265037366764334399624707440423524248}\cdot t^{51}+\frac{7104524789780551725113958878990540526441162683011418771475}{19449269060149467057337598498829761694096992}\cdot t^{49}-\frac{137347881935704000828805383558205225443770814301122881048975}{4862317265037366764334399624707440423524248}\cdot t^{47}+\frac{136225030077824242056945151147516656506629406165660079899778375}{77797076240597868229350393995319046776387968}\cdot t^{45}-\frac{6849464950283612590715736629139007614306416598201452469381974625}{77797076240597868229350393995319046776387968}\cdot t^{43}+\frac{1126453347454579727886235855371893835374113352402793144211343692875}{311188304962391472917401575981276187105551872}\cdot t^{41}-\frac{464292343665048217436617112180204604441578834430151844712443557125}{3794979328809652108748799707088733989092096}\cdot t^{39}+\frac{103513522988254305850290077338888588004066961206115386106502186759875}{30359834630477216869990397656709871912736768}\cdot t^{37}-\frac{2381460560036095679805441828518829360041754545334523307170372343731875}{30359834630477216869990397656709871912736768}\cdot t^{35}+\frac{180824174189963282809991480176352741258971989798260184560678669785299375}{121439338521908867479961590626839487650947072}\cdot t^{33}-\frac{353277913165937519375353473054859533910502658987081274180823233574330625}{15179917315238608434995198828354935956368384}\cdot t^{31}+\frac{144953201275424224422236436449157293883796939085681345240525300414312630625}{485757354087635469919846362507357950603788288}\cdot t^{29}-\frac{52302371534873876727587499446733047239951510278576517018488963951750324375}{16750253589228809307580909051977860365647872}\cdot t^{27}+\frac{1774094695596567023909655387331844164806036522237100173451113743929573640625}{67001014356915237230323636207911441462591488}\cdot t^{25}-\frac{6042175644137366255919063971747359754285032444364030281786917643997881265625}{33500507178457618615161818103955720731295744}\cdot t^{23}+\frac{261567756972267595430364504113390202302167792060319371858439842308384210890625}{268004057427660948921294544831645765850365952}\cdot t^{21}-\frac{1109265401154535010512145953177330298250942677182437688275847316045248115953125}{268004057427660948921294544831645765850365952}\cdot t^{19}+\frac{14503136277338632222152035048984599922482415036399307940868990512953374522203125}{1072016229710643795685178179326583063401463808}\cdot t^{17}-\frac{8949578006759614029767647715845808758609377886595710455874554713393671118671875}{268004057427660948921294544831645765850365952}\cdot t^{15}+\frac{260231886104716472977789104310904195217620818212022764565102776326036103089765625}{4288064918842575182740712717306332253605855232}\cdot t^{13}-\frac{337240483924836073225395744165901448003822272137708192914802713505153556330734375}{4288064918842575182740712717306332253605855232}\cdot t^{11}+\frac{1195121162964850220699971417571689444132233699107239286990483146642295248356703125}{17152259675370300730962850869225329014423420928}\cdot t^9-\frac{340844649636304612989817760199941778210212963206462399009543928191617321447234375}{8576129837685150365481425434612664507211710464}\cdot t^7+\frac{909025020591112703069735275940144566896002107503670700138611240165627501661953125}{68609038701481202923851403476901316057693683712}\cdot t^5-\frac{147343858277835657413934035102180541539366095303463757986279571278383079365078125}{68609038701481202923851403476901316057693683712}\cdot t^3+\frac{29629035212755729957334471157149415749227676737539465019795262217994311734765625}{274436154805924811695405613907605264230774734848}\cdot t$

Warning: This rule has negative weights!

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.