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

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{15/4}, {-(11/2), -(23/4)}, z] == (1/(3635977185225 z^(1/4))) (Sqrt[2] ((3635977185225 - 6840810830700 z + 1609602548400 z^2 + 1352893449600 z^3 + 313934987520 z^4 + 47028731904 z^5 + 9113567232 z^6 + 37786484736 z^7 + 1694498816 z^8) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (3635977185225 - 1992841250400 z - 1970941896000 z^2 - 545050598400 z^3 - 90369861120 z^4 - 12239732736 z^5 + 1271660544 z^6 + 6207569920 z^7 + 33554432 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (3635977185225 + 2855128329900 z + 912473100000 z^2 + 170328312000 z^3 + 25348055040 z^4 + 4715741184 z^5 + 5086642176 z^6 + 398458880 z^7) 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]