Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.2328)

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=-1/2, b_1`>=-11/2

For fixed z and a₁=-1/2, b₁=11/2

http://functions.wolfram.com/07.22.03.2328.01

Input Form

HypergeometricPFQ[{-(1/2)}, {11/2, 6}, -z] == (1/(5632 z^(9/2))) (4 (2 Sqrt[z] (184320 - 235215 z + 78720 z^2 - 15008 z^3 + 3584 z^4 + 256 z^5) BesselJ[0, 2 Sqrt[z]] - (368640 - 290925 z + 88200 z^2 - 16576 z^3 + 3456 z^4 + 256 z^5) BesselJ[1, 2 Sqrt[z]]) + Pi Sqrt[z] (1091475 - 1039500 z + 332640 z^2 - 63360 z^3 + 14080 z^4 + 1024 z^5) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi Sqrt[z] (1091475 - 1039500 z + 332640 z^2 - 63360 z^3 + 14080 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]