Rule: Q[3, 12, 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.

• $P_1$:
  $8\cdot t^3-4\cdot t$
• $P_2$:
  $8\cdot t^{15}-28\cdot t^{13}+39\cdot t^{11}-\frac{55}{2}\cdot t^9+\frac{165}{16}\cdot t^7-\frac{63}{32}\cdot t^5+\frac{21}{128}\cdot t^3-\frac{1}{256}\cdot t$
• $P_3$:
  $8\cdot t^{31}-60\cdot t^{29}+203\cdot t^{27}-\frac{819}{2}\cdot t^{25}+\frac{8775}{16}\cdot t^{23}-\frac{16445}{32}\cdot t^{21}+\frac{44275}{128}\cdot t^{19}-\frac{43263}{256}\cdot t^{17}+\frac{245157}{4096}\cdot t^{15}-\frac{124355}{8192}\cdot t^{13}+\frac{88179}{32768}\cdot t^{11}-\frac{20995}{65536}\cdot t^9+\frac{12597}{524288}\cdot t^7-\frac{1071}{1048576}\cdot t^5+\frac{85}{4194304}\cdot t^3-\frac{1}{8388608}\cdot t$

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.