Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af3f)

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.af3f.01

Input Form

HypergeometricPFQ[{17/4}, {-(7/2), -(21/4)}, -z] == -((1/(12828304125 Sqrt[2])) (z^(1/4) ((-12828304125 + 28623699000 z - 22061192400 z^2 + 8000553600 z^3 - 2851430400 z^4 + 268369920 z^5 - 1668284416 z^6 + 8388608 z^7) BesselJ[-(1/4), Sqrt[z]]^2 + 12 Sqrt[z] (-4276101375 + 6120351900 z - 2761527600 z^2 + 855429120 z^3 - 413736960 z^4 - 656408576 z^5 + 34603008 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 4 z (12828304125 - 8098412400 z + 2718087840 z^2 - 855429120 z^3 - 336347136 z^4 - 391643136 z^5 + 2097152 z^6) 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]