Rule: Q[1, 6, 24, 32]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^7-3\cdot t^5+\frac{5}{4}\cdot t^3-\frac{1}{8}\cdot t$
• $P_3$:
  $2\cdot t^{31}-15\cdot t^{29}+\frac{203}{4}\cdot t^{27}-\frac{819}{8}\cdot t^{25}+\frac{8775}{64}\cdot t^{23}-\frac{16445}{128}\cdot t^{21}+\frac{44275}{512}\cdot t^{19}-\frac{43263}{1024}\cdot t^{17}+\frac{245157}{16384}\cdot t^{15}-\frac{124355}{32768}\cdot t^{13}+\frac{88179}{131072}\cdot t^{11}-\frac{20995}{262144}\cdot t^9+\frac{12597}{2097152}\cdot t^7-\frac{1071}{4194304}\cdot t^5+\frac{85}{16777216}\cdot t^3-\frac{1}{33554432}\cdot t$
• $P_4$:
  $2\cdot t^{63}-31\cdot t^{61}+\frac{915}{4}\cdot t^{59}-\frac{8555}{8}\cdot t^{57}+\frac{227563}{64}\cdot t^{55}-\frac{1145529}{128}\cdot t^{53}+\frac{9072063}{512}\cdot t^{51}-\frac{28989675}{1024}\cdot t^{49}+\frac{608783175}{16384}\cdot t^{47}-\frac{1329484065}{32768}\cdot t^{45}+\frac{4874774905}{131072}\cdot t^{43}-\frac{7550466105}{262144}\cdot t^{41}+\frac{39688347475}{2097152}\cdot t^{39}-\frac{44357564825}{4194304}\cdot t^{37}+\frac{84406109067}{16777216}\cdot t^{35}-\frac{68328754959}{33554432}\cdot t^{33}+\frac{751616304549}{1073741824}\cdot t^{31}-\frac{437423756715}{2147483648}\cdot t^{29}+\frac{428971123735}{8589934592}\cdot t^{27}-\frac{176103935007}{17179869184}\cdot t^{25}+\frac{240141729555}{137438953472}\cdot t^{23}-\frac{67282234305}{274877906944}\cdot t^{21}+\frac{30582833775}{1099511627776}\cdot t^{19}-\frac{5545773675}{2199023255552}\cdot t^{17}+\frac{6285210165}{35184372088832}\cdot t^{15}-\frac{676868787}{70368744177664}\cdot t^{13}+\frac{106874019}{281474976710656}\cdot t^{11}-\frac{5883955}{562949953421312}\cdot t^9+\frac{840565}{4503599627370496}\cdot t^7-\frac{17391}{9007199254740992}\cdot t^5+\frac{341}{36028797018963968}\cdot t^3-\frac{1}{72057594037927936}\cdot t$

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.