Rule: Q[2, 12, 15]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{14}-7\cdot t^{12}+\frac{77}{8}\cdot t^{10}-\frac{105}{16}\cdot t^8+\frac{147}{64}\cdot t^6-\frac{49}{128}\cdot t^4+\frac{49}{2048}\cdot t^2-\frac{1}{4096}$
• $P_3$:
  $2\cdot t^{29}-15\cdot t^{27}+\frac{101}{2}\cdot t^{25}-\frac{403}{4}\cdot t^{23}+\frac{16951}{128}\cdot t^{21}-\frac{30877}{256}\cdot t^{19}+\frac{9975}{128}\cdot t^{17}-\frac{18411}{512}\cdot t^{15}+\frac{192831}{16384}\cdot t^{13}-\frac{87737}{32768}\cdot t^{11}+\frac{26741}{65536}\cdot t^9-\frac{5135}{131072}\cdot t^7+\frac{17927}{8388608}\cdot t^5-\frac{917}{16777216}\cdot t^3+\frac{7}{16777216}\cdot t$

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.