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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] > Series representations > Generalized power series > Expansions at z==1 > The general formulas





http://functions.wolfram.com/07.28.06.0005.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] == (Product[Gamma[Subscript[b, k]], {k, 1, 3}]/ Product[Gamma[Subscript[a, k]], {k, 1, 4}]) (Sum[Subscript[g, k][0] (1 - z)^k, {k, 0, Infinity}] + (1 - z)^Subscript[\[Psi], 3] Sum[Subscript[g, k][Subscript[\[Psi], 3]] (1 - z)^k, {k, 0, Infinity}]) /; Subscript[g, k][r] == ((-1)^k/k!) Gamma[Subscript[a, 1] + r + k] Gamma[Subscript[a, 2] + r + k] Gamma[Subscript[\[Psi], 3] - 2 r - k] Sum[((Pochhammer[Subscript[\[Psi], 3] - r - k, j] Pochhammer[Subscript[b, 2] + Subscript[b, 3] - Subscript[a, 3] - Subscript[a, 4], j] Pochhammer[Subscript[b, 1] - Subscript[a, 3], j])/(j! Gamma[Subscript[\[Psi], 3] + Subscript[a, 1] + j] Gamma[Subscript[\[Psi], 3] + Subscript[a, 2] + j])) HypergeometricPFQ[{Subscript[b, 3] - Subscript[a, 4], Subscript[b, 2] - Subscript[a, 4], -j}, {Subscript[b, 2] + Subscript[b, 3] - Subscript[a, 3] - Subscript[a, 4], 1 - Subscript[b, 1] + Subscript[a, 3] - j}, 1], {j, 0, Infinity}] && Subscript[\[Psi], 3] == Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3] - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3] - Subscript[a, 4] && !Element[Subscript[\[Psi], 3], Integers] && Re[Subscript[a, 3]] > 0 && Re[Subscript[a, 4]] > 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)





2001-10-29





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