Rule: Q[1, 16, 18]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{17}-\frac{17}{4}\cdot t^{15}+\frac{119}{16}\cdot t^{13}-\frac{221}{32}\cdot t^{11}+\frac{935}{256}\cdot t^9-\frac{561}{512}\cdot t^7+\frac{357}{2048}\cdot t^5-\frac{51}{4096}\cdot t^3+\frac{17}{65536}\cdot t$
• $P_3$:
  $t^{35}-9\cdot t^{33}+\frac{593}{16}\cdot t^{31}-\frac{185}{2}\cdot t^{29}+\frac{39991}{256}\cdot t^{27}-\frac{48321}{256}\cdot t^{25}+\frac{344565}{2048}\cdot t^{23}-\frac{115115}{1024}\cdot t^{21}+\frac{3712775}{65536}\cdot t^{19}-\frac{1408451}{65536}\cdot t^{17}+\frac{3187041}{524288}\cdot t^{15}-\frac{165053}{131072}\cdot t^{13}+\frac{1557829}{8388608}\cdot t^{11}-\frac{156655}{8388608}\cdot t^9+\frac{80427}{67108864}\cdot t^7-\frac{1479}{33554432}\cdot t^5+\frac{3281}{4294967296}\cdot t^3-\frac{17}{4294967296}\cdot t$

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.