Rule: Q[13, 14, 28]

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.

• $P_1$:
  $8192\cdot t^{13}-24576\cdot t^{11}+28160\cdot t^9-15360\cdot t^7+4032\cdot t^5-448\cdot t^3+14\cdot t$
• $P_2$:
  $8192\cdot t^{27}-53248\cdot t^{25}+153600\cdot t^{23}-259072\cdot t^{21}+283360\cdot t^{19}-210672\cdot t^{17}+108528\cdot t^{15}-38760\cdot t^{13}+\frac{37791}{4}\cdot t^{11}-\frac{12155}{8}\cdot t^9+\frac{2431}{16}\cdot t^7-\frac{273}{32}\cdot t^5+\frac{455}{2048}\cdot t^3-\frac{7}{4096}\cdot t$
• $P_3$:
  $8192\cdot t^{55}-110592\cdot t^{53}+705536\cdot t^{51}-2828800\cdot t^{49}+7996800\cdot t^{47}-16950080\cdot t^{45}+27967632\cdot t^{43}-36814536\cdot t^{41}+\frac{314457495}{8}\cdot t^{39}-\frac{550858165}{16}\cdot t^{37}+\frac{1595093643}{64}\cdot t^{35}-\frac{1917334783}{128}\cdot t^{33}+\frac{1917334783}{256}\cdot t^{31}-\frac{1594920705}{512}\cdot t^{29}+\frac{2202509545}{2048}\cdot t^{27}-\frac{1257042033}{4096}\cdot t^{25}+\frac{18855630495}{262144}\cdot t^{23}-\frac{7195285845}{524288}\cdot t^{21}+\frac{4418157975}{2097152}\cdot t^{19}-\frac{1074687075}{4194304}\cdot t^{17}+\frac{405992895}{16777216}\cdot t^{15}-\frac{57998985}{33554432}\cdot t^{13}+\frac{12096045}{134217728}\cdot t^{11}-\frac{876525}{268435456}\cdot t^9+\frac{2629575}{34359738368}\cdot t^7-\frac{71253}{68719476736}\cdot t^5+\frac{1827}{274877906944}\cdot t^3-\frac{7}{549755813888}\cdot t$

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.