Rule: Q[1, 12, 14]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{13}-\frac{13}{4}\cdot t^{11}+\frac{65}{16}\cdot t^9-\frac{39}{16}\cdot t^7+\frac{91}{128}\cdot t^5-\frac{91}{1024}\cdot t^3+\frac{13}{4096}\cdot t$
• $P_3$:
  $t^{27}-7\cdot t^{25}+\frac{349}{16}\cdot t^{23}-\frac{319}{8}\cdot t^{21}+\frac{12145}{256}\cdot t^{19}-\frac{9861}{256}\cdot t^{17}+\frac{22287}{1024}\cdot t^{15}-\frac{2193}{256}\cdot t^{13}+\frac{75803}{32768}\cdot t^{11}-\frac{13585}{32768}\cdot t^9+\frac{48763}{1048576}\cdot t^7-\frac{1547}{524288}\cdot t^5+\frac{1469}{16777216}\cdot t^3-\frac{13}{16777216}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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