Rule: Q[2, 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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{42}-\frac{657685695148890279283238}{400553925549962741119}\cdot t^{40}+\frac{121995418447645220080113810}{400553925549962741119}\cdot t^{38}-\frac{713743112437750486816643295}{21081785555261196901}\cdot t^{36}+\frac{212682060501231966688864199925}{84327142221044787604}\cdot t^{34}-\frac{22500031553589037869420502487985}{168654284442089575208}\cdot t^{32}+\frac{218417071162378440455621231358645}{42163571110522393802}\cdot t^{30}-\frac{12697887153983788281906473228361225}{84327142221044787604}\cdot t^{28}+\frac{2234492843403737187409375518013257525}{674617137768358300832}\cdot t^{26}-\frac{74716958864330552955554329850725460625}{1349234275536716601664}\cdot t^{24}+\frac{948665797692660896514294037403416046625}{1349234275536716601664}\cdot t^{22}-\frac{18190988824208763407080704780203235469125}{2698468551073433203328}\cdot t^{20}+\frac{521233203400935519599772434539599908705625}{10793874204293732813312}\cdot t^{18}-\frac{5489386106722677714632642331464068939693125}{21587748408587465626624}\cdot t^{16}+\frac{10380553624359310892585195296731924131878125}{10793874204293732813312}\cdot t^{14}-\frac{54588697921498161873142685957981116584110625}{21587748408587465626624}\cdot t^{12}+\frac{1524667227222144642931861174821022483349300625}{345403974537399450025984}\cdot t^{10}-\frac{3303284355092249851897095122722945022001928125}{690807949074798900051968}\cdot t^8+\frac{1999421568215554916522695223133587143669471875}{690807949074798900051968}\cdot t^6-\frac{1128648924757389432818320013802101178248859375}{1381615898149597800103936}\cdot t^4+\frac{407284282659393937871233647709769609002565625}{5526463592598391200415744}\cdot t^2-\frac{6541867164969248383403585101822786240753125}{11052927185196782400831488}$

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.