Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0480)

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

For fixed z and a₁=-11/2, b₁=-1/2

http://functions.wolfram.com/07.22.03.0480.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(1/2), 1}, -z] == (1/498960) (-4 (2 (-62370 + 514152 z + 3442752 z^2 + 1978395 z^3 + 237148 z^4 + 7760 z^5 + 64 z^6) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (-219096 + 2629152 z + 1866321 z^2 + 233324 z^3 + 7728 z^4 + 64 z^5) BesselJ[1, 2 Sqrt[z]]) - Pi z^2 (12006225 + 7683984 z + 940896 z^2 + 30976 z^3 + 256 z^4) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] + Pi z^2 (12006225 + 7683984 z + 940896 z^2 + 30976 z^3 + 256 z^4) 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]