Rule: Q[12, 13]

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.

• $P_1$:
  $4096\cdot t^{12}-11264\cdot t^{10}+11520\cdot t^8-5376\cdot t^6+1120\cdot t^4-84\cdot t^2+1$
• $P_2$:
  $4096\cdot t^{25}-24576\cdot t^{23}+64768\cdot t^{21}-98560\cdot t^{19}+95760\cdot t^{17}-62016\cdot t^{15}+27132\cdot t^{13}-7956\cdot t^{11}+\frac{12155}{8}\cdot t^9-\frac{715}{4}\cdot t^7+\frac{3003}{256}\cdot t^5-\frac{91}{256}\cdot t^3+\frac{13}{4096}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.