Rule: Q[4, 9, 30]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{13}-66\cdot t^{11}+\frac{7569}{5}\cdot t^9-\frac{74484}{5}\cdot t^7+\frac{314307}{5}\cdot t^5-98658\cdot t^3+37611\cdot t$
• $P_3$:
  $t^{43}-\frac{2644215807758474485306420476511785400537336355360319067919}{3742279853373169184537541659615992497050465474333728299}\cdot t^{41}+\frac{468100809892931972792013969426838646024793431517144349909484}{2079044362985093991409745366453329165028036374629849055}\cdot t^{39}-\frac{28117983742049848429713528128995468284852465318656752065367784}{655041374639139202772933471622281791721162145431322305}\cdot t^{37}+\frac{2881567745338180246832140574342392198630693082820668758248031190441}{525998223835228779826665577712692278752093202781351810915}\cdot t^{35}-\frac{4745301864268152753535985620756219000174308978400980345188863342863}{9563604069731432360484828685685314159128967323297305653}\cdot t^{33}+\frac{3471259403731020490546814244459225978787572670277430692874349719468696}{105199644767045755965333115542538455750418640556270362183}\cdot t^{31}-\frac{172996001888939835475703986153784430629544652515686530529669593036146888}{105199644767045755965333115542538455750418640556270362183}\cdot t^{29}+\frac{6537861675465381441725912405873706255351776660883941472454826491835963118}{105199644767045755965333115542538455750418640556270362183}\cdot t^{27}-\frac{188414136438212301278177905418030433473006431793094204833128203867672723174}{105199644767045755965333115542538455750418640556270362183}\cdot t^{25}+\frac{180129874236551204005635493321367683798601292895845876851353730178238366800}{4573897598567206781101439806197324163061680024185667921}\cdot t^{23}-\frac{273650570695034033497934651653311051523862471797235786494101105648414060600}{415808872597018798281949073290665833005607274925969811}\cdot t^{21}+\frac{3446143216916896383806319476214846325353925146435573220636643897129844509850}{415808872597018798281949073290665833005607274925969811}\cdot t^{19}-\frac{32271494482957320142997594759541926232777006926731376712394731225541976291850}{415808872597018798281949073290665833005607274925969811}\cdot t^{17}+\frac{220490602680907608237944047826571522071671035477808932974567406658942204921800}{415808872597018798281949073290665833005607274925969811}\cdot t^{15}-\frac{1070688806835954672753583769984694390619091858871704765148129022052028920283000}{415808872597018798281949073290665833005607274925969811}\cdot t^{13}+\frac{3564862886922773342415208303641124748013721703242879435157549777923234207440375}{415808872597018798281949073290665833005607274925969811}\cdot t^{11}-\frac{7741443024254950983608160035652282151475358493691173252918640435699397210298875}{415808872597018798281949073290665833005607274925969811}\cdot t^9+\frac{139778041176480902850660050267511969015861138770141052485830324598244206056500}{5696011953383819154547247579324189493227496916794107}\cdot t^7-\frac{7320170395783704957394700509916697318469572089878700557796388089204983283406000}{415808872597018798281949073290665833005607274925969811}\cdot t^5+\frac{2385615365261982802356954766028850916696658687318298919930367849522250547348125}{415808872597018798281949073290665833005607274925969811}\cdot t^3-\frac{239773608652933945420898189867943007336270399240784270269645330250346076768125}{415808872597018798281949073290665833005607274925969811}\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.