Rule: Q[1, 2, 4, 96]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-1\cdot t$
• $P_3$:
  $2\cdot t^7-3\cdot t^5+\frac{5}{4}\cdot t^3-\frac{1}{8}\cdot t$
• $P_4$:
  $2\cdot t^{103}-51\cdot t^{101}+\frac{2525}{4}\cdot t^{99}-\frac{40425}{8}\cdot t^{97}+\frac{470547}{16}\cdot t^{95}-\frac{4244429}{32}\cdot t^{93}+\frac{61760773}{128}\cdot t^{91}-\frac{372474765}{256}\cdot t^{89}+\frac{121550931645}{32768}\cdot t^{87}-\frac{531838637759}{65536}\cdot t^{85}+\frac{4039710503829}{262144}\cdot t^{83}-\frac{13438059476569}{524288}\cdot t^{81}+\frac{78875566492905}{2097152}\cdot t^{79}-\frac{205423178668335}{4194304}\cdot t^{77}+\frac{954076540926267}{16777216}\cdot t^{75}-\frac{1983192809790555}{33554432}\cdot t^{73}+\frac{118450697821126785}{2147483648}\cdot t^{71}-\frac{199019597082826275}{4294967296}\cdot t^{69}+\frac{603229941545620725}{17179869184}\cdot t^{67}-\frac{825846068580413265}{34359738368}\cdot t^{65}+\frac{511238042454541545}{34359738368}\cdot t^{63}-\frac{572832987328582695}{68719476736}\cdot t^{61}+\frac{1162177790256437175}{274877906944}\cdot t^{59}-\frac{1067357058040130975}{549755813888}\cdot t^{57}+\frac{28391697743867483935}{35184372088832}\cdot t^{55}-\frac{21347681594756057541}{70368744177664}\cdot t^{53}+\frac{29010951910822334607}{281474976710656}\cdot t^{51}-\frac{17791709324818892075}{562949953421312}\cdot t^{49}+\frac{19664520832694564925}{2251799813685248}\cdot t^{47}-\frac{9773492882824287211}{4503599627370496}\cdot t^{45}+\frac{8716899057654093999}{18014398509481984}\cdot t^{43}-\frac{3478285395078058719}{36028797018963968}\cdot t^{41}+\frac{79227611776778004155}{4611686018427387904}\cdot t^{39}-\frac{25056619857700597985}{9223372036854775808}\cdot t^{37}+\frac{14023284727082855679}{36893488147419103232}\cdot t^{35}-\frac{3455012179136355747}{73786976294838206464}\cdot t^{33}+\frac{745198705303919867}{147573952589676412928}\cdot t^{31}-\frac{139781120599565445}{295147905179352825856}\cdot t^{29}+\frac{45256088487578605}{1180591620717411303424}\cdot t^{27}-\frac{6266227636741653}{2361183241434822606848}\cdot t^{25}+\frac{93993414551124795}{604462909807314587353088}\cdot t^{23}-\frac{9206478467454345}{1208925819614629174706176}\cdot t^{21}+\frac{1484915881847475}{4835703278458516698824704}\cdot t^{19}-\frac{96805419670575}{9671406556917033397649408}\cdot t^{17}+\frac{9973891723635}{38685626227668133590597632}\cdot t^{15}-\frac{394447695285}{77371252455336267181195264}\cdot t^{13}+\frac{23063658345}{309485009821345068724781056}\cdot t^{11}-\frac{473498025}{618970019642690137449562112}\cdot t^9+\frac{202927725}{39614081257132168796771975168}\cdot t^7-\frac{1581255}{79228162514264337593543950336}\cdot t^5+\frac{11713}{316912650057057350374175801344}\cdot t^3-\frac{13}{633825300114114700748351602688}\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.