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

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`=-9/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), 9/4}, z] == -((1/(99542520 Sqrt[2] z^(3/4))) ((2 Sqrt[z] (-131340825 + 184338000 z - 22176000 z^2 - 21762048 z^3 + 4100096 z^4 + 65536 z^5) BesselI[1/4, Sqrt[z]]^2 + (158991525 - 553014000 z - 310464000 z^2 + 314603520 z^3 - 38621184 z^4 + 4259840 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (158991525 + 184338000 z - 141926400 z^2 - 5537280 z^3 + 2551808 z^4 + 65536 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]