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

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=5/2

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

Input Form

HypergeometricPFQ[{17/4}, {5/2, -(17/4)}, z] == -((1/(7757100 Sqrt[2] z^(3/4))) ((48 z (-456035 - 624320 z + 52480 z^2 + 8192 z^3) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (10599435 + 22943040 z + 3855360 z^2 - 1294336 z^3 + 65536 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 5 (-6359661 - 10322928 z - 6468096 z^2 + 774144 z^3 + 65536 z^4) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^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]