Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9906)

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/07.22.03.9906.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(3/2), 17/4}, z] == ((-2 Sqrt[z] (123743795175 - 196832235600 z - 125346735360 z^2 + 111085793280 z^3 + 49194270720 z^4 + 128355139584 z^5 - 15149826048 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 + 3 (206239658625 - 474713038800 z + 185253868800 z^2 + 263685058560 z^3 + 140894208000 z^4 + 115495403520 z^5 - 14914945024 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (618718975875 - 104205301200 z + 132324192000 z^2 + 235134627840 z^3 + 131356753920 z^4 + 117257011200 z^5 - 14948499456 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (228898897920 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]