Rule: Q[4, 5, 10]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^9-\frac{855}{88}\cdot t^7+\frac{45297}{6292}\cdot t^5-\frac{24885}{12584}\cdot t^3+\frac{1845}{12584}\cdot t$
• $P_3$:
  $\frac{35}{8}\cdot t^{19}-\frac{253168212362648541839565}{11708192433819507315404}\cdot t^{17}+\frac{2198478180054710631324137587}{48682664139821511417449832}\cdot t^{15}-\frac{1560698298959239597472769455}{30136887324651411829849896}\cdot t^{13}+\frac{1890462290846455170733824875}{53319108343614036314349816}\cdot t^{11}-\frac{1501265945999485834157880623}{101791025019626796600122376}\cdot t^9+\frac{1051375538808820972670179}{290002920283837027350776}\cdot t^7-\frac{3926436962744550026756171}{8078652779335460047628760}\cdot t^5+\frac{12055752003614008885037}{403932638966773002381438}\cdot t^3-\frac{79715227995217817572411}{147031480583905372866843432}\cdot t$

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.