Rule: Q[12, 21]

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.

• $P_1$:
  $4096\cdot t^{12}-135168\cdot t^{10}+1520640\cdot t^8-7096320\cdot t^6+13305600\cdot t^4-7983360\cdot t^2+665280$
• $P_2$:
  $4096\cdot t^{33}-\frac{169531266432}{193249}\cdot t^{31}+\frac{205391409315840}{2512237}\cdot t^{29}-\frac{11005875364276320}{2512237}\cdot t^{27}+\frac{377600440796805600}{2512237}\cdot t^{25}-\frac{8744563582324768440}{2512237}\cdot t^{23}+\frac{20065862603796237360}{358891}\cdot t^{21}-\frac{226288979819213567850}{358891}\cdot t^{19}+\frac{94433917626447651450}{18889}\cdot t^{17}-\frac{1044815980504160192625}{37778}\cdot t^{15}+\frac{1982227677164601713550}{18889}\cdot t^{13}-\frac{3086482588843958417025}{11624}\cdot t^{11}+\frac{4986513451688993222625}{11624}\cdot t^9-\frac{19245077839616143717125}{46496}\cdot t^7+\frac{4975584239837721943125}{23248}\cdot t^5-\frac{9059923977142930439625}{185984}\cdot t^3+\frac{573488939085422196375}{185984}\cdot t$

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.