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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{42}-\frac{328842847574445139641619}{400553925549962741119}\cdot t^{40}+\frac{121995418447645220080113810}{400553925549962741119}\cdot t^{38}-\frac{1427486224875500973633286590}{21081785555261196901}\cdot t^{36}+\frac{212682060501231966688864199925}{21081785555261196901}\cdot t^{34}-\frac{22500031553589037869420502487985}{21081785555261196901}\cdot t^{32}+\frac{1747336569299027523644969850869160}{21081785555261196901}\cdot t^{30}-\frac{101583097231870306255251785826889800}{21081785555261196901}\cdot t^{28}+\frac{4468985686807474374818751036026515050}{21081785555261196901}\cdot t^{26}-\frac{149433917728661105911108659701450921250}{21081785555261196901}\cdot t^{24}+\frac{3794663190770643586057176149613664186500}{21081785555261196901}\cdot t^{22}-\frac{72763955296835053628322819120812941876500}{21081785555261196901}\cdot t^{20}+\frac{1042466406801871039199544869079199817411250}{21081785555261196901}\cdot t^{18}-\frac{10978772213445355429265284662928137879386250}{21081785555261196901}\cdot t^{16}+\frac{83044428994874487140681562373855393055025000}{21081785555261196901}\cdot t^{14}-\frac{436709583371985294985141487663848932672885000}{21081785555261196901}\cdot t^{12}+\frac{1524667227222144642931861174821022483349300625}{21081785555261196901}\cdot t^{10}-\frac{3303284355092249851897095122722945022001928125}{21081785555261196901}\cdot t^8+\frac{3998843136431109833045390446267174287338943750}{21081785555261196901}\cdot t^6-\frac{2257297849514778865636640027604202356497718750}{21081785555261196901}\cdot t^4+\frac{407284282659393937871233647709769609002565625}{21081785555261196901}\cdot t^2-\frac{6541867164969248383403585101822786240753125}{21081785555261196901}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.