Rule: Q[2, 3, 54]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^5-4\cdot t^3+\frac{3}{4}\cdot t$
• $P_3$:
  $4\cdot t^{59}-58\cdot t^{57}+399\cdot t^{55}-\frac{3465}{2}\cdot t^{53}+\frac{341055}{64}\cdot t^{51}-\frac{1581255}{128}\cdot t^{49}+\frac{2869685}{128}\cdot t^{47}-\frac{8361535}{256}\cdot t^{45}+\frac{318381525}{8192}\cdot t^{43}-\frac{626358425}{16384}\cdot t^{41}+\frac{1027227817}{32768}\cdot t^{39}-\frac{1412200023}{65536}\cdot t^{37}+\frac{52251400851}{4194304}\cdot t^{35}-\frac{50883115395}{8388608}\cdot t^{33}+\frac{10429458435}{4194304}\cdot t^{31}-\frac{7184738033}{8388608}\cdot t^{29}+\frac{132591074609}{536870912}\cdot t^{27}-\frac{63665481789}{1073741824}\cdot t^{25}+\frac{25264080075}{2147483648}\cdot t^{23}-\frac{8205150525}{4294967296}\cdot t^{21}+\frac{34461632205}{137438953472}\cdot t^{19}-\frac{7195285845}{274877906944}\cdot t^{17}+\frac{585262485}{274877906944}\cdot t^{15}-\frac{72212175}{549755813888}\cdot t^{13}+\frac{104306475}{17592186044416}\cdot t^{11}-\frac{6556407}{35184372088832}\cdot t^9+\frac{267003}{70368744177664}\cdot t^7-\frac{6293}{140737488355328}\cdot t^5+\frac{4495}{18014398509481984}\cdot t^3-\frac{15}{36028797018963968}\cdot t$

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.