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The Lommel Functions

The Lommel functions are a two-parameter family of functions that solve the Lommel differential equation and can be expanded in a series of Bessel functions. There are applications of these functions in optics.

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References
[1] A. P. Prudnikov, O. I. Marichev, and Yu. A. Brychkov, "The Lommel Functions and ," §1.5 in Integrals and Series, Vol. 3: More Special Functions, Newark, NJ: Gordon and Breach, 1990 pp. 28–29.
[2] NIST Digital Library of Mathematical Functions. "Lommel Functions." Version 1.0.8; Release date 2014-04-25. dlmf.nist.gov/11.9.
[3] F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark (eds.), NIST Handbook of Mathematical Functions, New York: Cambridge University Press, 2010.
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