Lommel function
The Lommel differential equation is an inhomogeneous form of the Bessel differential equation:
Two solutions are given by the Lommel functions sμ,ν(z) and Sμ,ν(z), introduced by Eugen von Lommel (1880),
where Jν(z) is a Bessel function of the first kind, and Yν(z) a Bessel function of the second kind.
See also
References
- Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G. (1953), Higher transcendental functions. Vol II (PDF), McGraw-Hill Book Company, Inc., New York-Toronto-London, MR 0058756
- Lommel, E. (1875), "Ueber eine mit den Bessel'schen Functionen verwandte Function", Math. Ann., 9 (3): 425–444, doi:10.1007/BF01443342
- Lommel, E. (1880), "Zur Theorie der Bessel'schen Funktionen IV", Math. Ann., 16 (2): 183–208, doi:10.1007/BF01446386
- Paris, R. B. (2010), "Lommel function", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W., NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0521192255, MR 2723248
- Solomentsev, E.D. (2001), "l/l060800", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
External links
- Weisstein, Eric W. "Lommel Differential Equation." From MathWorld—A Wolfram Web Resource.
- Weisstein, Eric W. "Lommel Function." From MathWorld—A Wolfram Web Resource.
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