Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0441)

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=-5/2

http://functions.wolfram.com/07.22.03.0441.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(5/2), 5}, z] == (1/(3273645375 z^(7/2))) (8 (2 BesselI[1, 2 Sqrt[z]] (-4214184975 - 2161120500 z + 206288775 z^2 + 43659000 z^3 + 6958800 z^4 + 1638144 z^5 + 910080 z^6 + 4040704 z^7 - 213504 z^8 + 2048 z^9 + 128 Pi z^(15/2) (31977 - 1672 z + 16 z^2) StruveL[0, 2 Sqrt[z]]) - Sqrt[z] BesselI[0, 2 Sqrt[z]] (-8428369950 - 108056025 z - 235758600 z^2 - 37422000 z^3 - 7038720 z^4 - 2518272 z^5 - 3938304 z^6 + 16584704 z^7 - 858112 z^8 + 8192 z^9 + 256 Pi z^7 (31977 - 1672 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]