Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0495)

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

For fixed z and a₁=-11/2, b₁=-1/2

http://functions.wolfram.com/07.22.03.0495.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(1/2), 5}, z] == (1/(654729075 z^(7/2))) (8 (BesselI[1, 2 Sqrt[z]] (-176818950 - 52390800 z + 4677750 z^2 + 26195400 z^3 + 33053760 z^4 + 206362368 z^5 - 52983108 z^6 + 3056560 z^7 - 53440 z^8 + 256 z^9 + Pi z^(11/2) (218243025 - 53721360 z + 3069792 z^2 - 53504 z^3 + 256 z^4) StruveL[0, 2 Sqrt[z]]) - Sqrt[z] BesselI[0, 2 Sqrt[z]] (-176818950 + 36018675 z - 28066500 z^2 - 34927200 z^3 - 92684160 z^4 + 462267648 z^5 - 108957912 z^6 + 6166240 z^7 - 107136 z^8 + 512 z^9 + Pi z^5 (218243025 - 53721360 z + 3069792 z^2 - 53504 z^3 + 256 z^4) 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]