Rule: Q[3, 28]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{31}-\frac{41516085547333}{2208427829322}\cdot t^{29}+\frac{8022287302181173}{125880386271354}\cdot t^{27}-\frac{7616809238253747}{59174540554910}\cdot t^{25}+\frac{108169967614894815}{627250129882046}\cdot t^{23}-\frac{2953483425267445}{18290312535154}\cdot t^{21}+\frac{105149018620602705}{969386564363162}\cdot t^{19}-\frac{52140490562462895}{987393745125326}\cdot t^{17}+\frac{18365233589740313}{987393745125326}\cdot t^{15}-\frac{28388247537583665}{6065418720055574}\cdot t^{13}+\frac{204108624919681105}{248682167522278534}\cdot t^{11}-\frac{6531081085531805}{67822409324257782}\cdot t^9+\frac{65180466604899285}{9201240198324305758}\cdot t^7-\frac{2700878827797633}{9201240198324305758}\cdot t^5+\frac{51857615932998145}{9210441438522630063758}\cdot t^3-\frac{291588326432565}{9210441438522630063758}\cdot t$

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.