Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9ne)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a9ne.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, -(23/4)}, z] == ((-4 z (13643761356225 + 464828106600 z + 23756971392 z^2 + 10952736768 z^3 + 567803904 z^4 + 8388608 z^5) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (22739602260375 + 2796011489700 z + 55991390400 z^2 + 5730975744 z^3 + 287571968 z^4 + 4194304 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-341094033905625 - 72259642026000 z - 3531323109600 z^2 + 112280947200 z^3 + 45547388928 z^4 + 2296381440 z^5 + 33554432 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(19964663136 Sqrt[2] z^(13/4))

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]