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

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`=-9/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(9/2), -(7/4)}, z] == -((1/(68762925 z^(1/4))) (Sqrt[2] (3 (-22920975 + 32016600 z - 2772000 z^2 + 68302080 z^3 - 127153152 z^4 + 122093568 z^5 + 4456448 z^6) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-68762925 + 4365900 z + 14968800 z^2 + 118883520 z^3 + 23768064 z^4 + 52248576 z^5 + 262144 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 12 z (-22920975 - 29106000 z - 27997200 z^2 - 25267200 z^3 + 18239488 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]