Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ge)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.a8ge.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(7/2), 13/4}, z] == (1/(1589575680 Sqrt[2] z^(7/4))) ((-2 Sqrt[z] (-885809925 - 124351920 z + 1080414720 z^2 + 251142144 z^3 + 22740992 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]]^2 + 3 (-1476349875 + 3491888400 z + 1340613120 z^2 + 272588800 z^3 + 23658496 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-4429049625 + 1027026000 z + 1294318080 z^2 + 269230080 z^3 + 23527424 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]