Rule: Q[1, 56, 58]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{57}-\frac{57}{4}\cdot t^{55}+\frac{1539}{16}\cdot t^{53}-\frac{13091}{32}\cdot t^{51}+\frac{314925}{256}\cdot t^{49}-\frac{712215}{256}\cdot t^{47}+\frac{5032055}{1024}\cdot t^{45}-\frac{14233527}{2048}\cdot t^{43}+\frac{262303569}{32768}\cdot t^{41}-\frac{1991564135}{262144}\cdot t^{39}+\frac{6279783081}{1048576}\cdot t^{37}-\frac{8265485241}{2097152}\cdot t^{35}+\frac{36429360877}{16777216}\cdot t^{33}-\frac{8406775587}{8388608}\cdot t^{31}+\frac{12987211455}{33554432}\cdot t^{29}-\frac{8369536271}{67108864}\cdot t^{27}+\frac{71651395881}{2147483648}\cdot t^{25}-\frac{63221819895}{8589934592}\cdot t^{23}+\frac{45570143685}{34359738368}\cdot t^{21}-\frac{13254473925}{68719476736}\cdot t^{19}+\frac{12251432655}{549755813888}\cdot t^{17}-\frac{1101980715}{549755813888}\cdot t^{15}+\frac{300540195}{2199023255552}\cdot t^{13}-\frac{29977155}{4398046511104}\cdot t^{11}+\frac{16653975}{70368744177664}\cdot t^9-\frac{5995431}{1125899906842624}\cdot t^7+\frac{312417}{4503599627370496}\cdot t^5-\frac{3857}{9007199254740992}\cdot t^3+\frac{57}{72057594037927936}\cdot t$
• $P_3$:
  $t^{115}-29\cdot t^{113}+\frac{6553}{16}\cdot t^{111}-\frac{15015}{4}\cdot t^{109}+\frac{6426531}{256}\cdot t^{107}-\frac{33430545}{256}\cdot t^{105}+\frac{1126561163}{2048}\cdot t^{103}-\frac{1974940643}{1024}\cdot t^{101}+\frac{376299136525}{65536}\cdot t^{99}-\frac{965686927205}{65536}\cdot t^{97}+\frac{8645291278855}{262144}\cdot t^{95}-\frac{2129044998955}{32768}\cdot t^{93}+\frac{476165369302455}{4194304}\cdot t^{91}-\frac{742421620175025}{4194304}\cdot t^{89}+\frac{8305367587711887}{33554432}\cdot t^{87}-\frac{5229904048702417}{16777216}\cdot t^{85}+\frac{761955208081136017}{2147483648}\cdot t^{83}-\frac{786093705107531429}{2147483648}\cdot t^{81}+\frac{23579204115729273255}{68719476736}\cdot t^{79}-\frac{5030222617592427411}{17179869184}\cdot t^{77}+\frac{250488161312164424649}{1099511627776}\cdot t^{75}-\frac{177930947569645213515}{1099511627776}\cdot t^{73}+\frac{923974240513201680465}{8796093022208}\cdot t^{71}-\frac{274214587857330809925}{4398046511104}\cdot t^{69}+\frac{9529021297663808398605}{281474976710656}\cdot t^{67}-\frac{4733806773298975596477}{281474976710656}\cdot t^{65}+\frac{4302801673794934104051}{562949953421312}\cdot t^{63}-\frac{27944353264972566093}{8796093022208}\cdot t^{61}+\frac{10871565780133899034815}{9007199254740992}\cdot t^{59}-\frac{3772494758053042728369}{9007199254740992}\cdot t^{57}+\frac{9555522272543180554695}{72057594037927936}\cdot t^{55}-\frac{1378524666698183006541}{36028797018963968}\cdot t^{53}+\frac{92649552125749259034537}{9223372036854775808}\cdot t^{51}-\frac{22093166755341763458325}{9223372036854775808}\cdot t^{49}+\frac{76404648305293558483415}{147573952589676412928}\cdot t^{47}-\frac{3733307371493250734365}{36893488147419103232}\cdot t^{45}+\frac{42112905191506924164005}{2361183241434822606848}\cdot t^{43}-\frac{6672888730264781681335}{2361183241434822606848}\cdot t^{41}+\frac{7577464366992912322525}{18889465931478580854784}\cdot t^{39}-\frac{479832437466723194301}{9444732965739290427392}\cdot t^{37}+\frac{3454263348172045978863}{604462909807314587353088}\cdot t^{35}-\frac{343296228235431431751}{604462909807314587353088}\cdot t^{33}+\frac{119862818931975642523}{2417851639229258349412352}\cdot t^{31}-\frac{1140837969150818785}{302231454903657293676544}\cdot t^{29}+\frac{9623045990488650979}{38685626227668133590597632}\cdot t^{27}-\frac{543827757824587509}{38685626227668133590597632}\cdot t^{25}+\frac{208597527059309115}{309485009821345068724781056}\cdot t^{23}-\frac{4189192308265965}{154742504910672534362390528}\cdot t^{21}+\frac{17769600161033175}{19807040628566084398385987584}\cdot t^{19}-\frac{476944215582195}{19807040628566084398385987584}\cdot t^{17}+\frac{648544433816871}{1267650600228229401496703205376}\cdot t^{15}-\frac{2648875549191}{316912650057057350374175801344}\cdot t^{13}+\frac{2050427055873}{20282409603651670423947251286016}\cdot t^{11}-\frac{17438315235}{20282409603651670423947251286016}\cdot t^9+\frac{774917033}{162259276829213363391578010288128}\cdot t^7-\frac{1253525}{81129638414606681695789005144064}\cdot t^5+\frac{123481}{5192296858534827628530496329220096}\cdot t^3-\frac{57}{5192296858534827628530496329220096}\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.