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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.22.0001.01

 Input Form

 LaplaceTransform[HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, -t], t, z] == (Pi z^(-1 + Subscript[a, 1]) Csc[Pi Subscript[a, 1]] Gamma[-Subscript[a, 1] + Subscript[a, 2]] Gamma[-Subscript[a, 1] + Subscript[a, 3]] Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] HypergeometricPFQ[ {1 + Subscript[a, 1] - Subscript[b, 1], 1 + Subscript[a, 1] - Subscript[b, 2]}, {1 + Subscript[a, 1] - Subscript[a, 2], 1 + Subscript[a, 1] - Subscript[a, 3]}, z])/ (Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[Subscript[a, 3]] Gamma[-Subscript[a, 1] + Subscript[b, 1]] Gamma[-Subscript[a, 1] + Subscript[b, 2]]) + (Pi z^(-1 + Subscript[a, 2]) Csc[Pi Subscript[a, 2]] Gamma[Subscript[a, 1] - Subscript[a, 2]] Gamma[-Subscript[a, 2] + Subscript[a, 3]] Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] HypergeometricPFQ[ {1 + Subscript[a, 2] - Subscript[b, 1], 1 + Subscript[a, 2] - Subscript[b, 2]}, {1 - Subscript[a, 1] + Subscript[a, 2], 1 + Subscript[a, 2] - Subscript[a, 3]}, z])/ (Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[Subscript[a, 3]] Gamma[-Subscript[a, 2] + Subscript[b, 1]] Gamma[-Subscript[a, 2] + Subscript[b, 2]]) + (Pi z^(-1 + Subscript[a, 3]) Csc[Pi Subscript[a, 3]] Gamma[Subscript[a, 1] - Subscript[a, 3]] Gamma[Subscript[a, 2] - Subscript[a, 3]] Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] HypergeometricPFQ[ {1 + Subscript[a, 3] - Subscript[b, 1], 1 + Subscript[a, 3] - Subscript[b, 2]}, {1 - Subscript[a, 1] + Subscript[a, 3], 1 - Subscript[a, 2] + Subscript[a, 3]}, z])/ (Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[Subscript[a, 3]] Gamma[-Subscript[a, 3] + Subscript[b, 1]] Gamma[-Subscript[a, 3] + Subscript[b, 2]]) + (HypergeometricPFQ[{1, 2 - Subscript[b, 1], 2 - Subscript[b, 2]}, {2 - Subscript[a, 1], 2 - Subscript[a, 2], 2 - Subscript[a, 3]}, z] (-1 + Subscript[b, 1]) (-1 + Subscript[b, 2]))/ ((-1 + Subscript[a, 1]) (-1 + Subscript[a, 2]) (-1 + Subscript[a, 3])) /; Re[z] > 0

 Standard Form

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 MathML Form

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2001-10-29