Rule: Q[1, 22, 92]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{23}-\frac{23}{4}\cdot t^{21}+\frac{115}{8}\cdot t^{19}-\frac{1311}{64}\cdot t^{17}+\frac{1173}{64}\cdot t^{15}-\frac{2737}{256}\cdot t^{13}+\frac{2093}{512}\cdot t^{11}-\frac{16445}{16384}\cdot t^9+\frac{9867}{65536}\cdot t^7-\frac{3289}{262144}\cdot t^5+\frac{253}{524288}\cdot t^3-\frac{23}{4194304}\cdot t$
• $P_3$:
  $t^{115}-\frac{115}{4}\cdot t^{113}+\frac{805}{2}\cdot t^{111}-\frac{234025}{64}\cdot t^{109}+\frac{6204825}{256}\cdot t^{107}-\frac{127954773}{1024}\cdot t^{105}+\frac{534123135}{1024}\cdot t^{103}-\frac{14845231895}{8192}\cdot t^{101}+\frac{350319724625}{65536}\cdot t^{99}-\frac{3562685501375}{262144}\cdot t^{97}+\frac{1974745677905}{65536}\cdot t^{95}-\frac{61659017145775}{1048576}\cdot t^{93}+\frac{426824070145025}{4194304}\cdot t^{91}-\frac{2636266315601625}{16777216}\cdot t^{89}+\frac{3650501729807625}{16777216}\cdot t^{87}-\frac{36417405256560867}{134217728}\cdot t^{85}+\frac{656616852353142905}{2147483648}\cdot t^{83}-\frac{2682433551689970355}{8589934592}\cdot t^{81}+\frac{1244427936351017175}{4294967296}\cdot t^{79}-\frac{67264604770131296775}{274877906944}\cdot t^{77}+\frac{207174982692004394067}{1099511627776}\cdot t^{75}-\frac{582482854073264633775}{4398046511104}\cdot t^{73}+\frac{374087228862301920225}{4398046511104}\cdot t^{71}-\frac{1757290668663176317125}{35184372088832}\cdot t^{69}+\frac{7550556609311010329625}{281474976710656}\cdot t^{67}-\frac{14839360589499238967823}{1125899906842624}\cdot t^{65}+\frac{833671943230294324035}{140737488355328}\cdot t^{63}-\frac{5482024596393147524715}{2251799813685248}\cdot t^{61}+\frac{8236539418226157611025}{9007199254740992}\cdot t^{59}-\frac{11301298271519611605825}{36028797018963968}\cdot t^{57}+\frac{3536641576734372573117}{36028797018963968}\cdot t^{55}-\frac{8067454287942462781995}{288230376151711744}\cdot t^{53}+\frac{66969590414365745262585}{9223372036854775808}\cdot t^{51}-\frac{63108815800677254404875}{36893488147419103232}\cdot t^{49}+\frac{6737106697675785328625}{18446744073709551616}\cdot t^{47}-\frac{41616070515357279658535}{590295810358705651712}\cdot t^{45}+\frac{28973213649932283306575}{2361183241434822606848}\cdot t^{43}-\frac{18130846795487769803075}{9444732965739290427392}\cdot t^{41}+\frac{2540549277563221332625}{9444732965739290427392}\cdot t^{39}-\frac{2540549277563221332625}{75557863725914323419136}\cdot t^{37}+\frac{2256007758476140543371}{604462909807314587353088}\cdot t^{35}-\frac{884854723990312210485}{2417851639229258349412352}\cdot t^{33}+\frac{19047753353998892985}{604462909807314587353088}\cdot t^{31}-\frac{22886835425347507075}{9671406556917033397649408}\cdot t^{29}+\frac{5948818938982770725}{38685626227668133590597632}\cdot t^{27}-\frac{1325736792116160333}{154742504910672534362390528}\cdot t^{25}+\frac{62652967491311925}{154742504910672534362390528}\cdot t^{23}-\frac{19838799468462975}{1237940039285380274899124224}\cdot t^{21}+\frac{10363551961137375}{19807040628566084398385987584}\cdot t^{19}-\frac{1095960040417125}{79228162514264337593543950336}\cdot t^{17}+\frac{11465428115133}{39614081257132168796771975168}\cdot t^{15}-\frac{23605293178215}{5070602400912917605986812821504}\cdot t^{13}+\frac{1124061579915}{20282409603651670423947251286016}\cdot t^{11}-\frac{37628354775}{81129638414606681695789005144064}\cdot t^9+\frac{205619425}{81129638414606681695789005144064}\cdot t^7-\frac{5233949}{649037107316853453566312041152512}\cdot t^5+\frac{63365}{5192296858534827628530496329220096}\cdot t^3-\frac{115}{20769187434139310514121985316880384}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev T (first kind) type can be downloaded here packed into a single file.