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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==infinity





http://functions.wolfram.com/07.04.06.0089.01









  


  










Input Form





ChebyshevT[\[Nu], z] == (-((2^(-1 - \[Nu]) (-1 + z)^\[Nu] \[Nu])/Sqrt[Pi])) Sum[Residue[((Gamma[-s - \[Nu]] Gamma[1/2 - s - \[Nu]])/ ((2/(z - 1))^s Gamma[1 - s - 2 \[Nu]])) Gamma[s], {s, -j}], {j, 0, Infinity}] + ((2^(-1 + \[Nu]) \[Nu])/((-1 + z)^\[Nu] Sqrt[Pi])) Sum[Residue[((Gamma[-s + \[Nu]] Gamma[1/2 - s + \[Nu]])/ ((2/(z - 1))^s Gamma[1 - s + 2 \[Nu]])) Gamma[s], {s, -j}], {j, 0, Infinity}] /; Abs[z - 1] > 2 && !Element[2 \[Nu], Integers]










Standard Form





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MathML Form







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Rule Form





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2007-05-02





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