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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/07.27.06.0039.01









  


  










Input Form





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