Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7qy)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a7qy.01

Input Form

HypergeometricPFQ[{-(17/4)}, {3/2, 9/4}, z] == ((2 Sqrt[z] (17650429335 - 45693703440 z + 25103586816 z^2 - 3268632576 z^3 + 117112832 z^4 - 1048576 z^5) BesselI[1/4, Sqrt[z]]^2 + 3 (-218243025 + 27862425360 z - 22409587200 z^2 + 3167707136 z^3 - 116195328 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-654729075 + 29755812240 z - 22764234240 z^2 + 3181830144 z^3 - 116326400 z^4 + 1048576 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(17519483520 Sqrt[2] z^(3/4))

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]