Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ad7o)

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`=11/2

http://functions.wolfram.com/07.22.03.ad7o.01

Input Form

HypergeometricPFQ[{7/4}, {11/2, -(11/4)}, z] == -((1/(3872 Sqrt[2] z^(13/4))) (15 (-4 z (30282525 + 3447600 z + 87296 z^2) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (151412625 + 30696900 z + 1507968 z^2 + 11264 z^3) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 17 (44533125 + 12987000 z + 1110720 z^2 + 22528 z^3) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]