Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0746)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=-7/2

http://functions.wolfram.com/07.22.03.0746.01

Input Form

HypergeometricPFQ[{-(9/2)}, {-(7/2), 3}, -z] == (1/(14189175 z^(3/2))) (2 (BesselJ[1, 2 Sqrt[z]] (9823275 + 1786050 z - 88200 z^2 + 7200 z^3 - 1152 z^4 + 512 z^5 - 2048 z^6 + 2048 Pi z^(13/2) StruveH[0, 2 Sqrt[z]]) - Sqrt[z] BesselJ[0, 2 Sqrt[z]] (9823275 - 396900 z + 25200 z^2 - 2880 z^3 + 768 z^4 - 1024 z^5 - 4096 z^6 + 2048 Pi z^6 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]