Rule: Q[2, 39]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{41}-\frac{1266194631996487348358}{298132551856770427}\cdot t^{39}+\frac{378549460575093139139769}{298132551856770427}\cdot t^{37}-\frac{3135218193437021981977311}{16115273073338942}\cdot t^{35}+\frac{297436009492121706478003095}{16115273073338942}\cdot t^{33}-\frac{19097240756740866880852226535}{16115273073338942}\cdot t^{31}+\frac{1742964166453072343624106448185}{32230546146677884}\cdot t^{29}-\frac{116341746107006195230965589714635}{64461092293355768}\cdot t^{27}+\frac{11547160316616675570159571226880885}{257844369173423072}\cdot t^{25}-\frac{429511080411451916960063731876751625}{515688738346846144}\cdot t^{23}+\frac{11995155468472737267344653098294085875}{1031377476693692288}\cdot t^{21}-\frac{250542993321136874315994153983848607625}{2062754953387384576}\cdot t^{19}+\frac{969311946972085086943983929029351966125}{1031377476693692288}\cdot t^{17}-\frac{21886887586510204314256070937047551444875}{4125509906774769152}\cdot t^{15}+\frac{176195900580495097224169739808030347758125}{8251019813549538304}\cdot t^{13}-\frac{978848750163251042875378527458661110334375}{16502039627099076608}\cdot t^{11}+\frac{14320333737984004227544773108839010669489375}{132016317016792612864}\cdot t^9-\frac{32149052812002296362347723102610089328689375}{264032634033585225728}\cdot t^7+\frac{39634808502789975185269365441115397759968125}{528065268067170451456}\cdot t^5-\frac{21980204592058212954982309085536328756034375}{1056130536134340902912}\cdot t^3+\frac{1732498774224917133302502990154841507090625}{1056130536134340902912}\cdot t$

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.