Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0807)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=-3/2

http://functions.wolfram.com/07.22.03.0807.01

Input Form

HypergeometricPFQ[{-(9/2)}, {-(3/2), 4}, z] == (1/(2027025 z^(5/2))) (2 (BesselI[1, 2 Sqrt[z]] (1786050 + 297675 z + 340200 z^2 + 121680 z^3 + 80640 z^4 + 384768 z^5 - 34432 z^6 + 512 z^7 + 32 Pi z^(11/2) (12285 - 1080 z + 16 z^2) StruveL[0, 2 Sqrt[z]]) - 2 Sqrt[z] BesselI[0, 2 Sqrt[z]] (893025 - 297675 z - 113400 z^2 - 52560 z^3 - 92160 z^4 + 401664 z^5 - 34688 z^6 + 512 z^7 + 16 Pi z^5 (12285 - 1080 z + 16 z^2) 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]