Rule: Q[1, 22, 38]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{23}-253\cdot t^{21}+26565\cdot t^{19}-1514205\cdot t^{17}+51482970\cdot t^{15}-1081142370\cdot t^{13}+14054850810\cdot t^{11}-110430970650\cdot t^9+496939367925\cdot t^7-1159525191825\cdot t^5+1159525191825\cdot t^3-316234143225\cdot t$
• $P_3$:
  $t^{61}-\frac{1022611450644699413430127163258571869}{758974758347076231570764048418186}\cdot t^{59}+\frac{1233382930727918279473768309058053682909}{1459566842975146599174546246958050}\cdot t^{57}-\frac{4151430932986201264461425778730492898771831}{12649579305784603859512734140303100}\cdot t^{55}+\frac{1120457175045612193644679441528579759193248751}{12649579305784603859512734140303100}\cdot t^{53}-\frac{44715754519396708454966686215256727529659387581}{2529915861156920771902546828060620}\cdot t^{51}+\frac{2284070534334229849305757791927896249353170966439}{843305287052306923967515609353540}\cdot t^{49}-\frac{45936993287754455949735495549778823086842474250149}{140550881175384487327919268225590}\cdot t^{47}+\frac{4441226376706374487914927836501716004450663580634543}{140550881175384487327919268225590}\cdot t^{45}-\frac{174101246280858729271376110895047809516487934036193714}{70275440587692243663959634112795}\cdot t^{43}+\frac{2232568749587461509075424638850164240460586953144676652}{14055088117538448732791926822559}\cdot t^{41}-\frac{470903675704104170376244474997665089701215022885952058365}{56220352470153794931167707290236}\cdot t^{39}+\frac{1576300078011349090057482777016815288129740066363823756609}{4324642497704138071628285176172}\cdot t^{37}-\frac{56695780476539678755951014460127410777582332648109386223659}{4324642497704138071628285176172}\cdot t^{35}+\frac{1685325356303511942911460881306156389191454244620397709996819}{4324642497704138071628285176172}\cdot t^{33}-\frac{10333903177844793205695472444858950344261030964177031958885655}{1081160624426034517907071294043}\cdot t^{31}+\frac{208466468068136127363133195030354159760100908599361899765952940}{1081160624426034517907071294043}\cdot t^{29}-\frac{6885054089803541704612066312149739886618282020534528304157207495}{2162321248852069035814142588086}\cdot t^{27}+\frac{92472772443061835348903865915413747402818752566491546134906432075}{2162321248852069035814142588086}\cdot t^{25}-\frac{2003426696365094459762825984658432488140574710519060526990812738725}{4324642497704138071628285176172}\cdot t^{23}+\frac{17318033050371925841347938629126000887188647203876970460792366880125}{4324642497704138071628285176172}\cdot t^{21}-\frac{117866348616128760547425755555351705736139355979782517365474788804875}{4324642497704138071628285176172}\cdot t^{19}+\frac{621008289315102283717436307302900297326848383383837702910255036857875}{4324642497704138071628285176172}\cdot t^{17}-\frac{1239493550570826701724094778006617872017147591014944615204082919860125}{2162321248852069035814142588086}\cdot t^{15}+\frac{3645938568684221069169668353839830098247861383048528246388561634133875}{2162321248852069035814142588086}\cdot t^{13}-\frac{3808154861741871138372420610015821121944977257649138276945048744450625}{1081160624426034517907071294043}\cdot t^{11}+\frac{5369368540347360468150581007274043847621474673565124986216377516704375}{1081160624426034517907071294043}\cdot t^9-\frac{18964341089642951574292569777307359762874747521995057012225263510764375}{4324642497704138071628285176172}\cdot t^7+\frac{9271636300008381574681591985582291537096006606691456689128388425284375}{4324642497704138071628285176172}\cdot t^5-\frac{1966286603320798098596118003397128383007297431202945638774951620303125}{4324642497704138071628285176172}\cdot t^3+\frac{91112778854295652373889111602546018731285016284285541680280964478125}{4324642497704138071628285176172}\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.