Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9sp)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.a9sp.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(7/2), 23/4}, -z] == (19 (2 Sqrt[z] (-5771092201875 + 5383021644000 z - 220540320000 z^2 + 7984005120 z^3 + 3973775360 z^4 - 522190848 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (17313276605625 - 42531200712000 z + 6630912288000 z^2 - 75277762560 z^3 - 4328325120 z^4 + 532676608 z^5 - 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (17313276605625 - 5596210620000 z + 320518598400 z^2 + 6755696640 z^3 + 4110876672 z^4 - 526385152 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(104689827840 Sqrt[2] z^(17/4))

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]