Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ab1u)

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=-1/4, b_1`>=-11/2

For fixed z and a₁=-1/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ab1u.01

Input Form

HypergeometricPFQ[{-(1/4)}, {-(11/2), 17/4}, z] == -((1/(242221056 Sqrt[2] z^(11/4))) (13 (6 Sqrt[z] (1267389585 - 1351882224 z - 123495680 z^2 + 684032 z^3) BesselI[1/4, Sqrt[z]]^2 + (-19010843775 + 33797055600 z + 7675202304 z^2 + 255332352 z^3 + 1048576 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 18 Sqrt[z] (2112315975 + 751045680 z + 62760192 z^2 + 1626112 z^3) 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]