Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1942)

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=-3/2, b_1`>=-11/2

For fixed z and a₁=-3/2, b₁=2

http://functions.wolfram.com/07.22.03.1942.01

Input Form

HypergeometricPFQ[{-(3/2)}, {2, 7/2}, -z] == (1/(6144 z^2)) (4 (2 z (-45 + 1308 z + 976 z^2 + 64 z^3) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (-135 + 876 z + 944 z^2 + 64 z^3) BesselJ[1, 2 Sqrt[z]]) + Pi (-135 - 720 z + 4320 z^2 + 3840 z^3 + 256 z^4) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] + Pi (135 + 720 z - 4320 z^2 - 3840 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]