Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1533)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-5/2, b_1`>=-11/2

For fixed z and a₁=-5/2, b₁=1/2

http://functions.wolfram.com/07.22.03.1533.01

Input Form

HypergeometricPFQ[{-(5/2)}, {1/2, 2}, z] == (1/(210 Sqrt[z])) (2 (2 Sqrt[z] (45 - 296 z + 142 z^2 - 8 z^3) BesselI[0, 2 Sqrt[z]] + (15 + 232 z - 138 z^2 + 8 z^3) BesselI[1, 2 Sqrt[z]]) + Pi z^(3/2) (525 - 280 z + 16 z^2) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(3/2) (-525 + 280 z - 16 z^2) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

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]