Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.3268)

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=3/2, b_1`>=-11/2

For fixed z and a₁=3/2, b₁=11/2

http://functions.wolfram.com/07.22.03.3268.01

Input Form

HypergeometricPFQ[{3/2}, {11/2, 6}, z] == (1/(32 z^(9/2))) (45 (-4 (2 Sqrt[z] (2304 + 1509 z + 248 z^2 + 16 z^3) BesselI[0, 2 Sqrt[z]] - (4608 + 1647 z + 256 z^2 + 16 z^3) BesselI[1, 2 Sqrt[z]]) + Pi Sqrt[z] (11025 + 6300 z + 1008 z^2 + 64 z^3) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] - Pi Sqrt[z] (11025 + 6300 z + 1008 z^2 + 64 z^3) 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]