Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8r3)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8r3.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, 13/4}, -z] == ((2 z (-4549860315 + 30597923664 z + 27886763520 z^2 + 3765510144 z^3 + 127205376 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]]^2 - 3 Sqrt[z] (-7193911725 + 10998907920 z + 24772898304 z^2 + 3655753728 z^3 + 126287872 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 (1459458000 - 8738504775 z + 13031338320 z^2 + 25184687616 z^3 + 3671138304 z^4 + 126418944 z^5 + 1048576 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(23025606912 Sqrt[2] z^(9/4))

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]