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variants of this functions
ChebyshevU






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevU[nu,z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/07.05.06.0044.01









  


  










Input Form





ChebyshevU[\[Nu], z] == (Sin[2 Pi \[Nu]]/(4 Sqrt[Pi])) Sum[(1/k!) ((Gamma[k - \[Nu]] Gamma[2 + k + \[Nu]] ((-2 I Floor[(Pi + Arg[1 + Subscript[z, 0]])/(2 Pi)] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)])/ E^((1/2) I Pi Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) - 1/((1/(1 + Subscript[z, 0]))^((1/2) Floor[Arg[z - Subscript[z, 0]]/ (2 Pi)]) (1 + Subscript[z, 0])^((1/2) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]))) Hypergeometric2F1Regularized[k - \[Nu], 2 + k + \[Nu], 3/2 + k, (1 + Subscript[z, 0])/2])/2^k - (Pi Sec[Pi \[Nu]] Sqrt[2] (1 + Subscript[z, 0])^(-2^(-1) - k) Hypergeometric2F1Regularized[3/2 + \[Nu], -(1/2) - \[Nu], 1/2 - k, (1 + Subscript[z, 0])/2])/((1/(1 + Subscript[z, 0]))^ ((1/2) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) (1 + Subscript[z, 0])^((1/2) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]))) (z - Subscript[z, 0])^k, {k, 0, Infinity}]










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





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