Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1562)

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=-5/2, b_1`>=-11/2

For fixed z and a₁=-5/2, b₁=1

http://functions.wolfram.com/07.22.03.1562.01

Input Form

HypergeometricPFQ[{-(5/2)}, {1, 7/2}, -z] == (1/(122880 z^2)) (4 (2 z (675 + 16680 z + 37952 z^2 + 8064 z^3 + 256 z^4) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (2025 + 3600 z + 34144 z^2 + 7936 z^3 + 256 z^4) BesselJ[1, 2 Sqrt[z]]) + Pi (2025 + 4500 z + 36000 z^2 + 144000 z^3 + 32000 z^4 + 1024 z^5) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (2025 + 4500 z + 36000 z^2 + 144000 z^3 + 32000 z^4 + 1024 z^5) BesselJ[0, 2 Sqrt[z]] StruveH[1, 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]