Lommel Function

The Lommel differential equation is an inhomogeneous form of the Bessel differential equation:

Two solutions are given by the Lommel functions s_μ,ν(z) and S_μ,νz), introduced by Eugen von Lommel (1880),

where J_ν(z) is a Bessel function of the first kind, and Yν(z) a Bessel function of the second kind.

See also

* Anger function
* Lommel polynomial
* Struve function
* Weber function

References

* Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G. (1953), Higher transcendental functions. Vol II, McGraw-Hill Book Company, Inc., New York-Toronto-London, MR0058756
* Lommel, E. (1875), "Ueber eine mit den Bessel'schen Functionen verwandte Function", Math. Ann. 9: 425–444, doi:10.1007/BF01443342
* Lommel, E. (1880), "Zur Theorie der Bessel'schen Funktionen IV", Math. Ann. 16: 183–208, doi:10.1007/BF01446386
* Paris, R. B. (2010), "Lommel function", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F. et al., NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0521192255, http://dlmf.nist.gov/11.9
* Solomentsev, E.D. (2001), "Lommel function", in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Springer, ISBN 978-1556080104, http://eom.springer.de/l/l060800.htm

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