Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1289)

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=3

http://functions.wolfram.com/07.22.03.1289.01

Input Form

HypergeometricPFQ[{-(7/2)}, {3, 4}, z] == (1/(468242775 z^2)) (16 (2 z (3274425 + 22318380 z - 16329600 z^2 + 2005824 z^3 - 64256 z^4 + 512 z^5) BesselI[0, Sqrt[z]]^2 - Sqrt[z] (12006225 + 25740540 z - 29856960 z^2 + 3916992 z^3 - 127744 z^4 + 1024 z^5) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] - 2 (1091475 + 6776280 z + 15474060 z^2 - 15373296 z^3 + 1974080 z^4 - 64000 z^5 + 512 z^6) BesselI[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]