Rule: Q[4, 5, 10, 20]

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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^9-32\cdot t^7+21\cdot t^5-5\cdot t^3+\frac{5}{16}\cdot t$
• $P_3$:
  $16\cdot t^{19}-72\cdot t^{17}+136\cdot t^{15}-140\cdot t^{13}+\frac{1365}{16}\cdot t^{11}-\frac{1001}{32}\cdot t^9+\frac{429}{64}\cdot t^7-\frac{99}{128}\cdot t^5+\frac{165}{4096}\cdot t^3-\frac{5}{8192}\cdot t$
• $P_4$:
  $16\cdot t^{39}-152\cdot t^{37}+666\cdot t^{35}-1785\cdot t^{33}+\frac{6545}{2}\cdot t^{31}-\frac{17391}{4}\cdot t^{29}+\frac{69223}{16}\cdot t^{27}-\frac{105183}{32}\cdot t^{25}+\frac{7888725}{4096}\cdot t^{23}-\frac{7153575}{8192}\cdot t^{21}+\frac{10015005}{32768}\cdot t^{19}-\frac{5368545}{65536}\cdot t^{17}+\frac{4345965}{262144}\cdot t^{15}-\frac{1300075}{524288}\cdot t^{13}+\frac{557175}{2097152}\cdot t^{11}-\frac{81719}{4194304}\cdot t^9+\frac{245157}{268435456}\cdot t^7-\frac{13167}{536870912}\cdot t^5+\frac{665}{2147483648}\cdot t^3-\frac{5}{4294967296}\cdot t$

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.