Rule: Q[1, 2, 24, 56]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-1\cdot t$
• $P_3$:
  $2\cdot t^{27}-13\cdot t^{25}+\frac{75}{2}\cdot t^{23}-\frac{253}{4}\cdot t^{21}+\frac{8855}{128}\cdot t^{19}-\frac{13167}{256}\cdot t^{17}+\frac{6783}{256}\cdot t^{15}-\frac{4845}{512}\cdot t^{13}+\frac{37791}{16384}\cdot t^{11}-\frac{12155}{32768}\cdot t^9+\frac{2431}{65536}\cdot t^7-\frac{273}{131072}\cdot t^5+\frac{455}{8388608}\cdot t^3-\frac{7}{16777216}\cdot t$
• $P_4$:
  $2\cdot t^{83}-41\cdot t^{81}+405\cdot t^{79}-\frac{5135}{2}\cdot t^{77}+\frac{1502501}{128}\cdot t^{75}-\frac{10555545}{256}\cdot t^{73}+\frac{59273445}{512}\cdot t^{71}-\frac{273273675}{1024}\cdot t^{69}+\frac{16871053725}{32768}\cdot t^{67}-\frac{55262073757}{65536}\cdot t^{65}+\frac{19416404293}{16384}\cdot t^{63}-\frac{47223209943}{32768}\cdot t^{61}+\frac{1600342114735}{1048576}\cdot t^{59}-\frac{2966614689395}{2097152}\cdot t^{57}+\frac{4831343922729}{4194304}\cdot t^{55}-\frac{6931928236959}{8388608}\cdot t^{53}+\frac{280946973839103}{536870912}\cdot t^{51}-\frac{314492881163175}{1073741824}\cdot t^{49}+\frac{155658092696925}{1073741824}\cdot t^{47}-\frac{136248095712855}{2147483648}\cdot t^{45}+\frac{13488561475572645}{549755813888}\cdot t^{43}-\frac{9206478467454345}{1099511627776}\cdot t^{41}+\frac{5534686468704225}{2199023255552}\cdot t^{39}-\frac{2923166552608575}{4398046511104}\cdot t^{37}+\frac{21631432489303455}{140737488355328}\cdot t^{35}-\frac{8725899885515631}{281474976710656}\cdot t^{33}+\frac{763805560270599}{140737488355328}\cdot t^{31}-\frac{230779457781565}{281474976710656}\cdot t^{29}+\frac{956086325095055}{9007199254740992}\cdot t^{27}-\frac{210398934237219}{18014398509481984}\cdot t^{25}+\frac{38962765599485}{36028797018963968}\cdot t^{23}-\frac{5999744185435}{72057594037927936}\cdot t^{21}+\frac{48459472266975}{9223372036854775808}\cdot t^{19}-\frac{4923689695575}{18446744073709551616}\cdot t^{17}+\frac{196947587823}{18446744073709551616}\cdot t^{15}-\frac{12058015581}{36893488147419103232}\cdot t^{13}+\frac{17417133617}{2361183241434822606848}\cdot t^{11}-\frac{550858165}{4722366482869645213696}\cdot t^9+\frac{11344905}{9444732965739290427392}\cdot t^7-\frac{135751}{18889465931478580854784}\cdot t^5+\frac{12341}{604462909807314587353088}\cdot t^3-\frac{21}{1208925819614629174706176}\cdot t$

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.