From Wikipedia, the free encyclopedia
The Lommel differential equation, named after
Eugen von Lommel, is an inhomogeneous form of the
Bessel differential equation:
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.
The s function can also be written as
[1]
where pFq is a
generalized hypergeometric function.
See also
References
-
^ Watson's "Treatise on the Theory of Bessel functions" (1966), Section 10.7, Equation (10)
- 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. (eds.),
NIST Handbook of Mathematical Functions, Cambridge University Press,
ISBN
978-0-521-19225-5,
MR
2723248.
- Solomentsev, E.D. (2001) [1994],
"Lommel function",
Encyclopedia of Mathematics,
EMS Press
External links