Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.2320)

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=5

http://functions.wolfram.com/07.22.03.2320.01

Input Form

HypergeometricPFQ[{-(1/2)}, {5, 5}, -z] == (1/(99225 z^(7/2))) (512 (2 Sqrt[z] (-2835 + 2664 z - 882 z^2 + 336 z^3 + 32 z^4) BesselJ[0, Sqrt[z]]^2 + (11340 - 7137 z + 2160 z^2 - 624 z^3 - 64 z^4) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + Sqrt[z] (-9873 + 6516 z - 2052 z^2 + 640 z^3 + 64 z^4) BesselJ[1, Sqrt[z]]^2))

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]