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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=5/2

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

Input Form

HypergeometricPFQ[{19/4}, {5/2, -(23/4)}, z] == (1/(1748906775 z^(1/4))) (Sqrt[2] ((1748906775 - 5165884080 z + 1202019840 z^2 + 381394944 z^3 - 34406400 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]]^2 + 64 Sqrt[z] (194476275 - 6133680 z - 46690560 z^2 + 1204224 z^3 + 131072 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-6813568125 - 1838516400 z + 3638638080 z^2 + 293314560 z^3 - 39911424 z^4 + 1048576 z^5) 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]