Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8oq)

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.a8oq.01

Input Form

HypergeometricPFQ[{-(13/4)}, {7/2, -(23/4)}, z] == ((-16 z (3298467249 + 3266516736 z + 400963584 z^2 + 16973824 z^3 + 262144 z^4) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (38973609675 + 7603235472 z + 832405504 z^2 + 34406400 z^3 + 524288 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-584604145125 + 37792591200 z + 57355812864 z^2 + 6623232000 z^3 + 274726912 z^4 + 4194304 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (20380593618 Sqrt[2] z^(5/4))

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]