Rule: Q[1, 10, 12]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{11}-\frac{55}{21}\cdot t^9+\frac{330}{133}\cdot t^7-\frac{330}{323}\cdot t^5+\frac{55}{323}\cdot t^3-\frac{33}{4199}\cdot t$
• $P_3$:
  $t^{23}-\frac{3013}{525}\cdot t^{21}+\frac{510163}{35625}\cdot t^{19}-\frac{1412064599}{69328125}\cdot t^{17}+\frac{172465288538}{9481640625}\cdot t^{15}-\frac{119660941144034}{11298955078125}\cdot t^{13}+\frac{7640345597881498}{1890402099609375}\cdot t^{11}-\frac{306400099580342}{309338525390625}\cdot t^9+\frac{35679608200027}{240596630859375}\cdot t^7-\frac{8055482927839}{653047998046875}\cdot t^5+\frac{15773922604559}{33305447900390625}\cdot t^3-\frac{298379692913}{55509079833984375}\cdot t$

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.