Rule: Q[3, 8, 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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{11}-\frac{10483}{1482}\cdot t^9+\frac{1617}{221}\cdot t^7-\frac{69993}{20995}\cdot t^5+\frac{68299}{109174}\cdot t^3-\frac{3633}{109174}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{21}-\frac{54418441}{4226664}\cdot t^{19}+\frac{919573982789}{32356670112}\cdot t^{17}-\frac{2859045169344287}{81424608670080}\cdot t^{15}+\frac{1397236827764554824509}{52528838964302817792}\cdot t^{13}-\frac{439898293384487743629047}{34572057398351916079104}\cdot t^{11}+\frac{1978358763710679622079863}{518580860975278741186560}\cdot t^9-\frac{28936702776416257135159}{42106992985172205480960}\cdot t^7+\frac{3157695912956870583506747}{46528227248615287056460800}\cdot t^5-\frac{8927475025208916680119}{2938624878859912866723840}\cdot t^3+\frac{9240863468472883881557}{241946781692799492693596160}\cdot t$

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.