Rule: Q[2, 6, 27]

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.

• $P_1$:
  $4\cdot t^2-1$
• $P_2$:
  $4\cdot t^8-7\cdot t^6+\frac{15}{4}\cdot t^4-\frac{5}{8}\cdot t^2+\frac{1}{64}$
• $P_3$:
  $4\cdot t^{35}-34\cdot t^{33}+132\cdot t^{31}-310\cdot t^{29}+\frac{31465}{64}\cdot t^{27}-\frac{71253}{128}\cdot t^{25}+\frac{118755}{256}\cdot t^{23}-\frac{148005}{512}\cdot t^{21}+\frac{2220075}{16384}\cdot t^{19}-\frac{1562275}{32768}\cdot t^{17}+\frac{408595}{32768}\cdot t^{15}-\frac{156009}{65536}\cdot t^{13}+\frac{676039}{2097152}\cdot t^{11}-\frac{124355}{4194304}\cdot t^9+\frac{14535}{8388608}\cdot t^7-\frac{969}{16777216}\cdot t^5+\frac{969}{1073741824}\cdot t^3-\frac{9}{2147483648}\cdot t$

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.