Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0433)

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/07.22.03.0433.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(5/2), 3}, z] == (1/(30405375 z^(3/2))) (2 (BesselI[1, 2 Sqrt[z]] (-9823275 + 6548850 z + 1598400 z^2 + 442080 z^3 + 264960 z^4 + 1214976 z^5 - 84224 z^6 + 1024 z^7 + 64 Pi z^(11/2) (19305 - 1320 z + 16 z^2) StruveL[0, 2 Sqrt[z]]) - Sqrt[z] BesselI[0, 2 Sqrt[z]] (-9823275 - 3742200 z - 896400 z^2 - 357120 z^3 - 587520 z^4 + 2512896 z^5 - 169472 z^6 + 2048 z^7 + 64 Pi z^5 (19305 - 1320 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]