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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-3/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(3/2), -(7/4)}, z] == (1/(4147605 z^(1/4))) (Sqrt[2] (3 (1382535 + 263340 z + 22120560 z^2 + 511230720 z^3 + 163205120 z^4 + 2686976 z^5) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (4147605 + 6320160 z + 73735200 z^2 + 480499200 z^3 + 42983424 z^4 + 131072 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 12 z (1382535 + 3950100 z + 29494080 z^2 + 30530560 z^3 + 638976 z^4) 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]