Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0896)

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=3/2

http://functions.wolfram.com/07.22.03.0896.01

Input Form

HypergeometricPFQ[{-(9/2)}, {3/2, 3}, -z] == (1/(129729600 z^(3/2))) (4 (2 Sqrt[z] (226800 + 19051200 z + 46376055 z^2 + 16569720 z^3 + 1450752 z^4 + 37504 z^5 + 256 z^6) BesselJ[0, 2 Sqrt[z]] - (453600 + 5443200 z + 39203685 z^2 + 15876000 z^3 + 1432224 z^4 + 37376 z^5 + 256 z^6) BesselJ[1, 2 Sqrt[z]]) + Pi z^(3/2) (42567525 + 170270100 z + 64864800 z^2 + 5765760 z^3 + 149760 z^4 + 1024 z^5) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi z^(3/2) (42567525 + 170270100 z + 64864800 z^2 + 5765760 z^3 + 149760 z^4 + 1024 z^5) 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]