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variants of this functions
ChebyshevT




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevT[nu,z] > Series representations > Residue representations > General case > Expansions at z==1





http://functions.wolfram.com/07.04.06.0084.01









  


  








Input Form





ChebyshevT[\[Nu], z] == (-((2^(-1 + \[Nu]) \[Nu])/((-1 + z)^\[Nu] Sqrt[Pi]))) ((Sin[Pi \[Nu]] Sum[Residue[((Gamma[-s - \[Nu]] Gamma[-s + \[Nu]])/ (((z - 1)/2)^s Gamma[1/2 - s])) Gamma[s], {s, -j}], {j, 0, Infinity}])/(2^\[Nu] (1/(z - 1))^\[Nu]) - 2^(-(1/2) - \[Nu]) (1/(z - 1))^(-(1/2) - \[Nu]) Cos[Pi \[Nu]] Sum[Residue[((Gamma[1/2 - s - \[Nu]] Gamma[1/2 - s + \[Nu]])/ (((z - 1)/2)^s Gamma[3/2 - s])) Gamma[s], {s, -j}], {j, 0, Infinity}]) - ((2^(-1 - \[Nu]) (-1 + z)^\[Nu] \[Nu])/Sqrt[Pi]) (2^\[Nu] (1/(z - 1))^\[Nu] Sin[Pi \[Nu]] Sum[Residue[((Gamma[-s - \[Nu]] Gamma[-s + \[Nu]])/ (((z - 1)/2)^s Gamma[1/2 - s])) Gamma[s], {s, -j}], {j, 0, Infinity}] + 2^(-(1/2) + \[Nu]) (1/(z - 1))^(-(1/2) + \[Nu]) Cos[Pi \[Nu]] Sum[Residue[((Gamma[1/2 - s - \[Nu]] Gamma[1/2 - s + \[Nu]])/(((z - 1)/2)^s Gamma[3/2 - s])) Gamma[s], {s, -j}], {j, 0, Infinity}]) /; Abs[z - 1] < 2








Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02