Rule: Q[4, 50]

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.

• $P_1$:
  $16\cdot t^4-12\cdot t^2+1$
• $P_2$:
  $16\cdot t^{54}-212\cdot t^{52}+1326\cdot t^{50}-\frac{20825}{4}\cdot t^{48}+\frac{57575}{4}\cdot t^{46}-\frac{476721}{16}\cdot t^{44}+\frac{1533939}{32}\cdot t^{42}-\frac{62891499}{1024}\cdot t^{40}+\frac{260932815}{4096}\cdot t^{38}-\frac{886163135}{16384}\cdot t^{36}+\frac{1240628389}{32768}\cdot t^{34}-\frac{5752004349}{262144}\cdot t^{32}+\frac{1382264611}{131072}\cdot t^{30}-\frac{2202509545}{524288}\cdot t^{28}+\frac{1450433115}{1048576}\cdot t^{26}-\frac{6285210165}{16777216}\cdot t^{24}+\frac{11119987215}{134217728}\cdot t^{22}-\frac{7952684355}{536870912}\cdot t^{20}+\frac{2268783825}{1073741824}\cdot t^{18}-\frac{2029964475}{8589934592}\cdot t^{16}+\frac{173996955}{8589934592}\cdot t^{14}-\frac{44352165}{34359738368}\cdot t^{12}+\frac{4032015}{68719476736}\cdot t^{10}-\frac{7888725}{4398046511104}\cdot t^8+\frac{593775}{17592186044416}\cdot t^6-\frac{23751}{70368744177664}\cdot t^4+\frac{189}{140737488355328}\cdot t^2-\frac{1}{1125899906842624}$

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.