Rule: Q[1, 4, 16]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{10}{9}\cdot t^3+\frac{5}{21}\cdot t$
• $P_3$:
  $t^{21}-\frac{35335620166}{7135347843}\cdot t^{19}+\frac{180709480704313}{17231865040845}\cdot t^{17}-\frac{96664607452792}{7789747210245}\cdot t^{15}+\frac{1734603690026}{192752697357}\cdot t^{13}-\frac{41778582658804}{10122121377423}\cdot t^{11}+\frac{37797535859134}{31699057228983}\cdot t^9-\frac{534118021610248}{2553535165668075}\cdot t^7+\frac{1205860438533401}{58731308810365725}\cdot t^5-\frac{234576601175962}{246671497003536045}\cdot t^3+\frac{1112587844447}{82223832334512015}\cdot t$

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.