Rule: Q[2, 6, 17]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{25}-\frac{239149773239839492962333175}{25734754719089366655711084}\cdot t^{23}+\frac{25345253038168927734987884425}{1003655434044485299572732276}\cdot t^{21}-\frac{1794391541078767846950438113725}{45387529072900612991789115148}\cdot t^{19}+\frac{5361627257342282710363159035845}{136162587218701838975367345444}\cdot t^{17}-\frac{482707493922767930722255469185}{18567625529822978042095547106}\cdot t^{15}+\frac{8609465606293013019801026425075}{748894229702860114364520399942}\cdot t^{13}-\frac{5616444660361327007293104688325}{1670610204721764870505468584486}\cdot t^{11}+\frac{39821591513000512507020723608300}{63559124606914418027867145691581}\cdot t^9-\frac{6255314720394519487593662581}{90250798163882737703751715572}\cdot t^7+\frac{112703017759093659954689342885}{28248499825295296901274286974036}\cdot t^5-\frac{7688844455560495605798379805}{84745499475885890703822860922108}\cdot t^3+\frac{9773188329258358180141025}{28248499825295296901274286974036}\cdot t$

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.