Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1197)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=1/2

http://functions.wolfram.com/07.22.03.1197.01

Input Form

HypergeometricPFQ[{-(7/2)}, {1/2, 7/2}, z] == (1/(36864 z^(5/2))) (-2 Sqrt[z] (945 - 1260 z - 10116 z^2 + 6060 z^3 - 500 z^4 + 8 z^5) Cosh[2 Sqrt[z]] + (945 + 6300 z^2 - 5604 z^3 + 492 z^4 - 8 z^5) Sinh[2 Sqrt[z]] + 16 z^3 (-3150 + 1575 z - 126 z^2 + 2 z^3) 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]