Rule: Q[1, 42]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{43}-903\cdot t^{41}+185115\cdot t^{39}-\frac{45723405}{2}\cdot t^{37}+\frac{15225893865}{8}\cdot t^{35}-\frac{1811881369935}{16}\cdot t^{33}+\frac{19930695069285}{4}\cdot t^{31}-\frac{1323967601031075}{8}\cdot t^{29}+\frac{268765423009308225}{64}\cdot t^{27}-\frac{10481851497363020775}{128}\cdot t^{25}+\frac{157227772460445311625}{128}\cdot t^{23}-\frac{3616238766590242167375}{256}\cdot t^{21}+\frac{126568356830658475858125}{1024}\cdot t^{19}-\frac{1664860693695584567056875}{2048}\cdot t^{17}+\frac{4043233113260705377138125}{1024}\cdot t^{15}-\frac{28302631792824937639966875}{2048}\cdot t^{13}+\frac{1103802639920172567958708125}{32768}\cdot t^{11}-\frac{3571126187977028896336996875}{65536}\cdot t^9+\frac{3571126187977028896336996875}{65536}\cdot t^7-\frac{3947034207764084569635628125}{131072}\cdot t^5+\frac{3947034207764084569635628125}{524288}\cdot t^3-\frac{563862029680583509947946875}{1048576}\cdot t$

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.