Airy-Fock Functions

Fok (1946) and Hazewinkel (1988, p. 65) call


where Ai(z) is an Airy function and omega=2^(epii/3), the Airy-Fock functions.

On the other hand, Fock (1965) and Kiselev et al. (2003) and Babich and Buldyrev (2008) use the notation v(z) to denote twice the quantity v(z) in equation (1), and term this function (alone) "the Airy-Fock function."

These three functions satisfy


where z^_ is the complex conjugate of z.

See also

Airy Functions

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Babich, V. M. and Kirpichnikova, N. Ya. The Boundary Layer Method in Diffraction Problems. New York: Springer-Verlag, 1979.Babich, M. and Buldyrev, V. S. Asymptotic Methods in Short-Wavelength Diffraction Theory. Alpha Science, 2008.Fock, V. A. Electromagnetic Diffraction and Propagation Problems. Oxford, England: Pergamon Press, 1965.Fok, V. A. Tables of Airy Functions. Moscow, 1946.Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet "Mathematical Encyclopaedia." Dordrecht, Netherlands: Reidel, p. 65, 1988.Kiselev, A. P.; Yarovoĭ, V. O.; and Vsemirnova, E. A. "Polarization Anomalies of Elastic Waves. Caustic and Penumbra." Zap. Nauchn. Sem. St.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 297, 2003. Published in Mat. Vopr. Teor. Rasprostr. Voln. 32, 136-153 and 275-27. Translation in J. Math. Sci. (N. Y.) 127, 2413-2423, 2005.

Referenced on Wolfram|Alpha

Airy-Fock Functions

Cite this as:

Weisstein, Eric W. "Airy-Fock Functions." From MathWorld--A Wolfram Web Resource.

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