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variants of this functions
ChebyshevT






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevT[nu,z] > Series representations > Generalized power series > Expansions at z==infinity > For the function itself > Expansions in 1/z





http://functions.wolfram.com/07.04.06.0068.01









  


  










Input Form





ChebyshevT[\[Nu], z] == Subscript[F, Infinity][z, \[Nu]] /; (Subscript[F, m][z, \[Nu]] == 2^(\[Nu] - 1) z^\[Nu] Sum[(Pochhammer[-(\[Nu]/2), k] Pochhammer[(1 - \[Nu])/2, k])/ (Pochhammer[1 - \[Nu], k] k!)/z^(2 k), {k, 0, m}] + (2^(-\[Nu] - 1) Sum[(Pochhammer[\[Nu]/2, k] Pochhammer[(1 + \[Nu])/2, k])/(Pochhammer[1 + \[Nu], k] k!)/z^(2 k), {k, 0, m}])/z^\[Nu] == ChebyshevT[\[Nu], z] + ((2^(-3 - 2 m + \[Nu]) z^(-2 (1 + m) + \[Nu]) \[Nu] Gamma[2 + 2 m - \[Nu]])/((m + 1)! Gamma[2 + m - \[Nu]])) HypergeometricPFQ[{1, 1 + m - \[Nu]/2, 3/2 + m - \[Nu]/2}, {2 + m, 2 + m - \[Nu]}, 1/z^2] - ((2^(-3 - 2 m - \[Nu]) z^(-2 (1 + m) - \[Nu]) \[Nu] Gamma[2 + 2 m + \[Nu]])/((m + 1)! Gamma[2 + m + \[Nu]])) HypergeometricPFQ[{1, 1 + m + \[Nu]/2, 3/2 + m + \[Nu]/2}, {2 + m, 2 + m + \[Nu]}, 1/z^2] && Element[m, Integers] && m >= 0) && !Element[\[Nu], Integers]










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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