Airy function [¦er·ē ¦fəŋk·shən]
Airy Function
(mathematics)
Either of the solutions of the Airy differential equation.
Airy Function
either of the functions Ai(z) and Bi(z), which are solutions of the second-order differential equation
W″ – zW = 0
where z is the independent variable.
The Airy functions of the argument (–z) may be expressed in terms of Bessel functions of order v = ±⅓:
The asymptotic representations for large |z| are
Airy functions play an important role in the theory of asymptotic representations of various special functions; they have diverse applications in mathematical physics—for example, in the theory of the diffraction of radio waves at the earth’s surface. Airy functions were studied by J. R. Airy in 1911.
REFERENCES
Lebedev, N. N. Spetsial’nye funktsii i ikh prilozheniia. 2nd ed. Moscow-Leningrad, 1963.Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content.
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