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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==-1 > For the function itself > General case





http://functions.wolfram.com/07.05.06.0069.01









  


  










Input Form





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