Rule: Q[3, 8, 26]

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.

• $P_1$:
  $t^3-3\cdot t$
• $P_2$:
  $t^{11}-\frac{149}{3}\cdot t^9+798\cdot t^7-4914\cdot t^5+10605\cdot t^3-5355\cdot t$
• $P_3$:
  $t^{37}-\frac{16818716006919620270534203439873}{31624247009580822942848348876}\cdot t^{35}+\frac{178703928418642798214093198316599291}{1423091115431137032428175699420}\cdot t^{33}-\frac{7857518111436990743742589424289629534}{450645519886526726935588971483}\cdot t^{31}+\frac{3582292774564155359839204121244265208818}{2253227599432633634677944857415}\cdot t^{29}-\frac{14329882756963165527527952067865243780369}{142309111543113703242817569942}\cdot t^{27}+\frac{6865736973134045560284981619404421741869969}{1502151732955089089785296571610}\cdot t^{25}-\frac{22716819594914183031335062408514336374577595}{150215173295508908978529657161}\cdot t^{23}+\frac{551986468747729814171787768965889124751719815}{150215173295508908978529657161}\cdot t^{21}-\frac{518345698913137458255400313022229316938443810}{7906061752395205735712087219}\cdot t^{19}+\frac{6743336074716238968073608084779238372671888550}{7906061752395205735712087219}\cdot t^{17}-\frac{63061317334489079972172707537281298422711963020}{7906061752395205735712087219}\cdot t^{15}+\frac{414442341419640115954909915830010636313767030500}{7906061752395205735712087219}\cdot t^{13}-\frac{3702672685663732146454581693531268299059123701275}{15812123504790411471424174438}\cdot t^{11}+\frac{10709821205191533477173530157596337825647795207725}{15812123504790411471424174438}\cdot t^9-\frac{9329870141149156706852741138743629491550190228125}{7906061752395205735712087219}\cdot t^7+\frac{8728839098009360002688730940988136114684240146850}{7906061752395205735712087219}\cdot t^5-\frac{14259268249997881297907747257575784666986435051375}{31624247009580822942848348876}\cdot t^3+\frac{1571565648912690099399168797165901199642315403625}{31624247009580822942848348876}\cdot t$

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.