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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==0 > For the function itself > General case





http://functions.wolfram.com/07.05.06.0057.01









  


  










Input Form





ChebyshevU[\[Nu], z] == Subscript[F, Infinity][z, \[Nu]] /; Subscript[F, m][z, \[Nu]] == Cos[(Pi \[Nu])/2] Sum[((Pochhammer[-(\[Nu]/2), k] Pochhammer[1 + \[Nu]/2, k])/(Pochhammer[1/2, k] k!)) z^(2 k), {k, 0, m}] + z (1 + \[Nu]) Sin[(Pi \[Nu])/2] Sum[((Pochhammer[(1 - \[Nu])/2, k] Pochhammer[(3 + \[Nu])/2, k])/ (Pochhammer[3/2, k] k!)) z^(2 k), {k, 0, m}] == ChebyshevU[\[Nu], z] - ((z^(2 m + 2) Cos[(Pi \[Nu])/2] Pochhammer[\[Nu]/2 + 1, m + 1] Pochhammer[-(\[Nu]/2), m + 1]) HypergeometricPFQ[{1, m - \[Nu]/2 + 1, m + \[Nu]/2 + 2}, {m + 3/2, m + 2}, z^2])/((m + 1)! Pochhammer[1/2, m + 1]) - ((z^(2 m + 3) (\[Nu] + 1) Sin[(Pi \[Nu])/2] Pochhammer[(1 - \[Nu])/2, m + 1] Pochhammer[(\[Nu] + 3)/2, m + 1]) HypergeometricPFQ[ {1, m - \[Nu]/2 + 3/2, m + \[Nu]/2 + 5/2}, {m + 2, m + 5/2}, z^2])/ ((m + 1)! Pochhammer[3/2, m + 1]) && Element[m, Integers] && m >= 0










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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