Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1180)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=-1/2

http://functions.wolfram.com/07.22.03.1180.01

Input Form

HypergeometricPFQ[{-(7/2)}, {-(1/2), 5}, -z] == (1/(675675 z^(7/2))) (8 (-2 BesselJ[1, 2 Sqrt[z]] (-297675 + 132300 z + 14175 z^2 - 12600 z^3 + 10320 z^4 - 52992 z^5 - 6688 z^6 - 128 z^7 + 8 Pi z^(11/2) (6825 + 840 z + 16 z^2) StruveH[0, 2 Sqrt[z]]) + Sqrt[z] BesselJ[0, 2 Sqrt[z]] (-595350 - 33075 z - 37800 z^2 + 25200 z^3 - 49920 z^4 - 225024 z^5 - 27008 z^6 - 512 z^7 + 16 Pi z^5 (6825 + 840 z + 16 z^2) 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]