Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a921)

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

For fixed z and a₁=-11/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a921.01

Input Form

HypergeometricPFQ[{-(11/4)}, {1/2, 23/4}, -z] == (19 (2 Sqrt[z] (-119401907625 + 80270190000 z + 14010796800 z^2 + 2767564800 z^3 + 42069196800 z^4 + 90455408640 z^5 + 12499025920 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - (-358205722875 + 786647862000 z + 60713452800 z^2 + 24908083200 z^3 + 3406233600 z^4 + 83094405120 z^5 + 12331253760 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (358205722875 - 22475653200 z + 7783776000 z^2 + 9580032000 z^3 + 23843635200 z^4 + 87435509760 z^5 + 12431917056 z^6 + 268435456 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (1766640844800 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]