Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1592)

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=3/2

http://functions.wolfram.com/07.22.03.1592.01

Input Form

HypergeometricPFQ[{-(5/2)}, {3/2, 6}, -z] == (1/(405405 z^(9/2))) (8 (BesselJ[1, 2 Sqrt[z]] (-113400 + 52650 z + 6075 z^2 - 1800 z^3 - 25200 z^4 - 34236 z^5 - 3584 z^6 - 64 z^7 + Pi z^(9/2) (32175 + 35100 z + 3600 z^2 + 64 z^3) StruveH[0, 2 Sqrt[z]]) - Sqrt[z] BesselJ[0, 2 Sqrt[z]] (-2 (56700 + 2025 z + 2700 z^2 + 3600 z^3 + 40320 z^4 + 35988 z^5 + 3616 z^6 + 64 z^7) + Pi z^4 (32175 + 35100 z + 3600 z^2 + 64 z^3) 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]