Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0568)

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=2

http://functions.wolfram.com/07.22.03.0568.01

Input Form

HypergeometricPFQ[{-(11/2)}, {2, 2}, -z] == (1/(18261468225 Sqrt[z])) (2 (Sqrt[z] (9833098275 + 25913238120 z + 12270334176 z^2 + 1554450048 z^3 + 65137920 z^4 + 953344 z^5 + 4096 z^6) BesselJ[0, Sqrt[z]]^2 - (1404728325 + 18783848160 z + 11205283104 z^2 + 1507163904 z^3 + 64429824 z^4 + 950272 z^5 + 4096 z^6) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + Sqrt[z] (2746431765 + 20768100984 z + 11539132416 z^2 + 1522583424 z^3 + 64664320 z^4 + 951296 z^5 + 4096 z^6) BesselJ[1, Sqrt[z]]^2))

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]