Rule: Q[1, 40]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{41}-820\cdot t^{39}+151905\cdot t^{37}-16861455\cdot t^{35}+\frac{10032565725}{8}\cdot t^{33}-66214933785\cdot t^{31}+\frac{10263314736675}{4}\cdot t^{29}-\frac{297636127363575}{4}\cdot t^{27}+\frac{104470280704614825}{64}\cdot t^{25}-\frac{870585672538456875}{32}\cdot t^{23}+\frac{44051635030445917875}{128}\cdot t^{21}-\frac{420492879836074670625}{128}\cdot t^{19}+\frac{23968094150656256225625}{1024}\cdot t^{17}-\frac{31342892350858181218125}{256}\cdot t^{15}+\frac{470143385262872718271875}{1024}\cdot t^{13}-\frac{1222372801683469067506875}{1024}\cdot t^{11}+\frac{67230504092590798712878125}{32768}\cdot t^9-\frac{35592619813724540495053125}{16384}\cdot t^7+\frac{83049446232023927821790625}{65536}\cdot t^5-\frac{21855117429479981005734375}{65536}\cdot t^3+\frac{13113070457687988603440625}{524288}\cdot t$

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.