Rule: Q[2, 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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{44}-\frac{7255566411573886299156499}{8017041162036390230920}\cdot t^{42}+\frac{2982078616002310072860882879}{8017041162036390230920}\cdot t^{40}-\frac{73856533187373614442307216401}{801704116203639023092}\cdot t^{38}+\frac{12333963179539269598533182249361}{801704116203639023092}\cdot t^{36}-\frac{2945285444152201867625379546494055}{1603408232407278046184}\cdot t^{34}+\frac{260155537620157478965307135034944403}{1603408232407278046184}\cdot t^{32}-\frac{2169352420735601880724822787615295591}{200426029050909755773}\cdot t^{30}+\frac{110624310583288718677139952583655350005}{200426029050909755773}\cdot t^{28}-\frac{17352733992565286295097767903242472377895}{801704116203639023092}\cdot t^{26}+\frac{523918973731987205204170772604002493535875}{801704116203639023092}\cdot t^{24}-\frac{6070420435761196327530694926605654509185675}{400852058101819511546}\cdot t^{22}+\frac{107184754620531148553124513090451096414734675}{400852058101819511546}\cdot t^{20}-\frac{2850406771077732443422122812355574656961933875}{801704116203639023092}\cdot t^{18}+\frac{28061519240162300456343655804789281537592851375}{801704116203639023092}\cdot t^{16}-\frac{49944328964235906990576796034813851505346279375}{200426029050909755773}\cdot t^{14}+\frac{248916960611337274326901970116529483383195243500}{200426029050909755773}\cdot t^{12}-\frac{6639617089763043117441550702971125787182311774875}{1603408232407278046184}\cdot t^{10}+\frac{13870415566052556639471835835219221990863457614375}{1603408232407278046184}\cdot t^8-\frac{8209738826724477726039848883270990168041889530625}{801704116203639023092}\cdot t^6+\frac{4649378585162935288299021942285336257111976140625}{801704116203639023092}\cdot t^4-\frac{1795116028732864161181804126924245650395734361875}{1603408232407278046184}\cdot t^2+\frac{42429286114339981190579026024662948552547899375}{1603408232407278046184}$

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.