Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1229)

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=1

http://functions.wolfram.com/07.22.03.1229.01

Input Form

HypergeometricPFQ[{-(7/2)}, {1, 6}, z] == (1/(241215975 z^4)) (32 (2 z (-3175200 + 893025 z - 363825 z^2 + 4013100 z^3 - 6541920 z^4 + 1269312 z^5 - 53504 z^6 + 512 z^7) BesselI[0, Sqrt[z]]^2 + Sqrt[z] (25401600 - 3969000 z + 1885275 z^2 - 1543500 z^3 + 11350080 z^4 - 2460096 z^5 + 106240 z^6 - 1024 z^7) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] - 2 (12700800 - 396900 z + 628425 z^2 - 639450 z^3 + 1543500 z^4 - 5945808 z^5 + 1242944 z^6 - 53248 z^7 + 512 z^8) 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]