Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.acff)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=5/4, b_1`>=-11/2

For fixed z and a₁=5/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.acff.01

Input Form

HypergeometricPFQ[{5/4}, {-(7/2), -(21/4)}, -z] == (1/(21928725 Sqrt[2])) (z^(1/4) ((21928725 - 45349200 z + 29455920 z^2 - 6689280 z^3 + 987136 z^4 - 131072 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (21928725 - 27806220 z + 8770320 z^2 - 1458432 z^3 + 225280 z^4 + 65536 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 4 z (21928725 - 10263240 z + 2119104 z^2 - 301056 z^3 + 16384 z^4) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^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]