Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa0p)

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`=5/2

http://functions.wolfram.com/07.22.03.aa0p.01

Input Form

HypergeometricPFQ[{-(7/4)}, {5/2, 23/4}, -z] == (19 (2 Sqrt[z] (-638512875 + 237837600 z + 9434880 z^2 - 1006387200 z^3 + 2971860992 z^4 + 622854144 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - (-1915538625 + 3632428800 z + 1003242240 z^2 - 2012774400 z^3 + 2610757632 z^4 + 612368384 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (1915538625 + 454053600 z + 588107520 z^2 - 1536933888 z^3 + 2822701056 z^4 + 618659840 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(63795363840 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]