Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agf1)

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.agf1.01

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), 13/4}, -z] == (1/(353928960 Sqrt[2] z^(7/4))) ((-2 Sqrt[z] (613253025 - 63201600 z - 842688000 z^2 + 101376000 z^3 + 65273856 z^4 + 5767168 z^5) BesselJ[1/4, Sqrt[z]]^2 + (3066265125 + 3634092000 z - 5056128000 z^2 + 2433024000 z^3 + 674365440 z^4 + 12976128 z^5 + 2097152 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-3066265125 + 2907273600 z - 1564992000 z^2 - 191692800 z^3 + 56770560 z^4 + 4980736 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^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]