Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9541)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9541.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, -(13/4)}, -z] == ((4 z (33229228725 + 42058119600 z - 27222624000 z^2 + 5956546560 z^3 - 825425920 z^4 + 145752064 z^5 + 8388608 z^6) BesselJ[-(1/4), Sqrt[z]]^ 2 - 4 Sqrt[z] (99687686175 + 36325119600 z - 16359033600 z^2 + 3309834240 z^3 - 451215360 z^4 + 70254592 z^5 + 4194304 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (299063058525 + 52010966700 z + 210650932800 z^2 - 116584473600 z^3 + 24817582080 z^4 - 3434348544 z^5 + 574619648 z^6 + 33554432 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(94481478000 Sqrt[2] z^(7/4))

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]