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

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`=-7/2

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

Input Form

HypergeometricPFQ[{9/4}, {-(7/2), -(17/4)}, z] == -((1/(5221125 Sqrt[2])) (z^(1/4) (5 (-1044225 - 2246400 z - 1600560 z^2 - 482560 z^3 - 143360 z^4 + 196608 z^5) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (5221125 + 7055100 z + 2730000 z^2 + 684800 z^3 + 307200 z^4 + 65536 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (-5221125 - 2878200 z - 798720 z^2 - 204800 z^3 + 229376 z^4) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^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]