Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1568)

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/07.22.03.1568.01

Input Form

HypergeometricPFQ[{-(5/2)}, {1, 5}, -z] == (1/(675675 z^3)) (16 (z (8100 + 3825 z + 45000 z^2 + 68160 z^3 + 10496 z^4 + 256 z^5) BesselJ[0, Sqrt[z]]^2 - 2 Sqrt[z] (16200 + 5625 z + 4500 z^2 + 30360 z^3 + 5152 z^4 + 128 z^5) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + (32400 + 7200 z + 7425 z^2 + 18000 z^3 + 63104 z^4 + 10368 z^5 + 256 z^6) BesselJ[1, Sqrt[z]]^2))

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]