Rule: Q[1, 42, 44]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{43}-21\cdot t^{41}+\frac{205}{2}\cdot t^{39}-\frac{1235}{4}\cdot t^{37}+\frac{82251}{128}\cdot t^{35}-\frac{250971}{256}\cdot t^{33}+\frac{145299}{128}\cdot t^{31}-\frac{260865}{256}\cdot t^{29}+\frac{5883955}{8192}\cdot t^{27}-\frac{6556407}{16384}\cdot t^{25}+\frac{5785065}{32768}\cdot t^{23}-\frac{4032015}{65536}\cdot t^{21}+\frac{141120525}{8388608}\cdot t^{19}-\frac{59879925}{16777216}\cdot t^{17}+\frac{9694845}{16777216}\cdot t^{15}-\frac{2340135}{33554432}\cdot t^{13}+\frac{13037895}{2147483648}\cdot t^{11}-\frac{1562275}{4294967296}\cdot t^9+\frac{120175}{8589934592}\cdot t^7-\frac{5313}{17179869184}\cdot t^5+\frac{1771}{549755813888}\cdot t^3-\frac{11}{1099511627776}\cdot t$
• $P_3$:
  $2\cdot t^{87}-43\cdot t^{85}+\frac{1785}{4}\cdot t^{83}-\frac{23821}{8}\cdot t^{81}+\frac{459405}{32}\cdot t^{79}-\frac{3410667}{64}\cdot t^{77}+\frac{40567527}{256}\cdot t^{75}-\frac{198544775}{512}\cdot t^{73}+\frac{26088783435}{32768}\cdot t^{71}-\frac{91182316225}{65536}\cdot t^{69}+\frac{548496702215}{262144}\cdot t^{67}-\frac{1431790092795}{524288}\cdot t^{65}+\frac{1632743088275}{524288}\cdot t^{63}-\frac{3270510001437}{1048576}\cdot t^{61}+\frac{11554118344845}{4194304}\cdot t^{59}-\frac{18053969395461}{8388608}\cdot t^{57}+\frac{800392643198771}{536870912}\cdot t^{55}-\frac{984741570132705}{1073741824}\cdot t^{53}+\frac{2153926799433123}{4294967296}\cdot t^{51}-\frac{2094780068098575}{8589934592}\cdot t^{49}+\frac{3622737294241065}{34359738368}\cdot t^{47}-\frac{2783353955276895}{68719476736}\cdot t^{45}+\frac{3795482666286675}{274877906944}\cdot t^{43}-\frac{2292522306124995}{549755813888}\cdot t^{41}+\frac{156655690918541325}{140737488355328}\cdot t^{39}-\frac{73702772679770871}{281474976710656}\cdot t^{37}+\frac{60900802239115881}{1125899906842624}\cdot t^{35}-\frac{22001200566043685}{2251799813685248}\cdot t^{33}+\frac{6914663035042301}{4503599627370496}\cdot t^{31}-\frac{1879204156221315}{9007199254740992}\cdot t^{29}+\frac{876961939569947}{36028797018963968}\cdot t^{27}-\frac{174201268131891}{72057594037927936}\cdot t^{25}+\frac{1866442158555975}{9223372036854775808}\cdot t^{23}-\frac{260170725132045}{18446744073709551616}\cdot t^{21}+\frac{59516178951775}{73786976294838206464}\cdot t^{19}-\frac{5486397089355}{147573952589676412928}\cdot t^{17}+\frac{797168807855}{590295810358705651712}\cdot t^{15}-\frac{44357564825}{1180591620717411303424}\cdot t^{13}+\frac{3641989533}{4722366482869645213696}\cdot t^{11}-\frac{104819165}{9444732965739290427392}\cdot t^9+\frac{62891499}{604462909807314587353088}\cdot t^7-\frac{685377}{1208925819614629174706176}\cdot t^5+\frac{7095}{4835703278458516698824704}\cdot t^3-\frac{11}{9671406556917033397649408}\cdot t$

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.