Airy-Fock Functions

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

			(1)
			(2)
			(3)

where  is an Airy function and , the Airy-Fock functions.

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

These three functions satisfy

(4)

(5)

where  is the complex conjugate of .

REFERENCES:

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.