Rule: Q[2, 39]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{41}-\frac{10193338076219}{662305587370}\cdot t^{39}+\frac{339338581007439}{4636139111590}\cdot t^{37}-\frac{7377634049849037}{34457790694250}\cdot t^{35}+\frac{15490866049760634}{35934553152575}\cdot t^{33}-\frac{146920893538483818}{231941206712075}\cdot t^{31}+\frac{3749178052481026698}{5334647754377725}\cdot t^{29}-\frac{30681168847995834714}{51060199934758225}\cdot t^{27}+\frac{715783624294642214103}{1787106997716537875}\cdot t^{25}-\frac{104699945860056716013}{500389959360630605}\cdot t^{23}+\frac{113693660636701599597}{1327121196565150735}\cdot t^{21}-\frac{306047402256384031581}{11185735799620556195}\cdot t^{19}+\frac{75505296148622743338}{11185735799620556195}\cdot t^{17}-\frac{70851950179778525274}{55928678998102780975}\cdot t^{15}+\frac{164751716624241183534}{931611995882683465955}\cdot t^{13}-\frac{115977012643524719466}{6521283971178784261685}\cdot t^{11}+\frac{71479078486729685109}{58098711743229168876830}\cdot t^9-\frac{149235933327366537639}{2730639451931770937211010}\cdot t^7+\frac{2724155672775810039}{1950456751379836383722150}\cdot t^5-\frac{5332041609931257}{316489208714464016981330}\cdot t^3+\frac{509347284035616}{8386964030933296450005245}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.