Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9596)

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/07.22.03.9596.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, -(5/4)}, z] == ((4 z (108356180625 - 44320122000 z + 87727622400 z^2 + 100504166400 z^3 + 100933632000 z^4 - 33768407040 z^5 + 1646264320 z^6 - 16777216 z^7) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-325068541875 + 71042548500 z - 63328003200 z^2 - 61699968000 z^3 - 41199206400 z^4 + 16383836160 z^5 - 817889280 z^6 + 8388608 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (975205625625 - 27374193000 z + 139738737600 z^2 - 461118873600 z^3 - 461058048000 z^4 - 372414873600 z^5 + 133453578240 z^6 - 6568280064 z^7 + 67108864 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(228416760000 Sqrt[2] z^(11/4))

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]