Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0939)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=5/2

http://functions.wolfram.com/07.22.03.0939.01

Input Form

HypergeometricPFQ[{-(9/2)}, {5/2, 11/2}, z] == (1/(188743680 z^(9/2))) (2 Sqrt[z] (-4465125 + 2764125 z - 5953500 z^2 - 14226030 z^3 + 20028510 z^4 - 3109986 z^5 + 135120 z^6 - 1940 z^7 + 8 z^8) Cosh[2 Sqrt[z]] + (4465125 + 3189375 z + 680400 z^2 - 4825170 z^3 + 17548650 z^4 - 2985030 z^5 + 133224 z^6 - 1932 z^7 + 8 z^8) Sinh[2 Sqrt[z]] - 32 z^3 (-893025 - 2679075 z + 2679075 z^2 - 396900 z^3 + 17010 z^4 - 243 z^5 + z^6) SinhIntegral[2 Sqrt[z]])

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

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]