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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{11}-\frac{596}{3}\cdot t^9+1596\cdot t^7-4914\cdot t^5+\frac{10605}{2}\cdot t^3-\frac{5355}{4}\cdot t$
• $P_3$:
  $8\cdot t^{37}-\frac{16818716006919620270534203439873}{7906061752395205735712087219}\cdot t^{35}+\frac{178703928418642798214093198316599291}{711545557715568516214087849710}\cdot t^{33}-\frac{7857518111436990743742589424289629534}{450645519886526726935588971483}\cdot t^{31}+\frac{1791146387282077679919602060622132604409}{2253227599432633634677944857415}\cdot t^{29}-\frac{14329882756963165527527952067865243780369}{569236446172454812971270279768}\cdot t^{27}+\frac{6865736973134045560284981619404421741869969}{12017213863640712718282372572880}\cdot t^{25}-\frac{22716819594914183031335062408514336374577595}{2403442772728142543656474514576}\cdot t^{23}+\frac{551986468747729814171787768965889124751719815}{4806885545456285087312949029152}\cdot t^{21}-\frac{259172849456568729127700156511114658469221905}{252993976076646583542786791008}\cdot t^{19}+\frac{3371668037358119484036804042389619186335944275}{505987952153293167085573582016}\cdot t^{17}-\frac{15765329333622269993043176884320324605677990755}{505987952153293167085573582016}\cdot t^{15}+\frac{103610585354910028988727478957502659078441757625}{1011975904306586334171147164032}\cdot t^{13}-\frac{3702672685663732146454581693531268299059123701275}{16191614468905381346738354624512}\cdot t^{11}+\frac{10709821205191533477173530157596337825647795207725}{32383228937810762693476709249024}\cdot t^9-\frac{9329870141149156706852741138743629491550190228125}{32383228937810762693476709249024}\cdot t^7+\frac{4364419549004680001344365470494068057342120073425}{32383228937810762693476709249024}\cdot t^5-\frac{14259268249997881297907747257575784666986435051375}{518131663004972203095627347984384}\cdot t^3+\frac{1571565648912690099399168797165901199642315403625}{1036263326009944406191254695968768}\cdot t$

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.