Rule: Q[1, 2, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{11}-\frac{10483}{3705}\cdot t^9+\frac{3234}{1105}\cdot t^7-\frac{139986}{104975}\cdot t^5+\frac{68299}{272935}\cdot t^3-\frac{3633}{272935}\cdot t$
• $P_4$:
  $t^{21}-\frac{54418441}{10566660}\cdot t^{19}+\frac{919573982789}{80891675280}\cdot t^{17}-\frac{2859045169344287}{203561521675200}\cdot t^{15}+\frac{1397236827764554824509}{131322097410757044480}\cdot t^{13}-\frac{439898293384487743629047}{86430143495879790197760}\cdot t^{11}+\frac{1978358763710679622079863}{1296452152438196852966400}\cdot t^9-\frac{28936702776416257135159}{105267482462930513702400}\cdot t^7+\frac{3157695912956870583506747}{116320568121538217641152000}\cdot t^5-\frac{8927475025208916680119}{7346562197149782166809600}\cdot t^3+\frac{9240863468472883881557}{604866954231998731733990400}\cdot t$

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.