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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 z==infinity > For the function itself > Expansions in 1/z





http://functions.wolfram.com/07.05.06.0077.01









  


  










Input Form





ChebyshevU[\[Nu], z] == Subscript[F, Infinity][z, \[Nu]] /; (Subscript[F, m][z, \[Nu]] == 2^\[Nu] z^\[Nu] Sum[(Pochhammer[-(\[Nu]/2), k] Pochhammer[(1 - \[Nu])/2, k])/(Pochhammer[-\[Nu], k] k!)/z^(2 k), {k, 0, m}] - 2^(-2 - \[Nu]) z^(-2 - \[Nu]) Sum[(Pochhammer[(3 + \[Nu])/2, k] Pochhammer[(2 + \[Nu])/2, k])/ (Pochhammer[2 + \[Nu], k] k!)/z^(2 k), {k, 0, m}] == ChebyshevU[\[Nu], z] - ((2^(-2 - 2 m + \[Nu]) z^(-2 - 2 m + \[Nu]) Gamma[2 + 2 m - \[Nu]])/(Gamma[2 + m] Gamma[1 + m - \[Nu]])) HypergeometricPFQ[{1, 1 + m - \[Nu]/2, 3/2 + m - \[Nu]/2}, {2 + m, 1 + m - \[Nu]}, 1/z^2] + ((2^(-4 - 2 m - \[Nu]) z^(-4 - 2 m - \[Nu]) Gamma[4 + 2 m + \[Nu]])/ (Gamma[2 + m] Gamma[3 + m + \[Nu]])) HypergeometricPFQ[ {1, 2 + m + \[Nu]/2, 5/2 + m + \[Nu]/2}, {2 + m, 3 + 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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