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Lommel function

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A solution of the non-homogeneous Bessel equation

If , where is a natural number, then

If the numbers and are not integers, then

If , where is an integer and is not an integer , then

Here, for the first sum is taken to be zero, and is a Bessel function (cf. Bessel functions). Lommel functions in two variables are also known.

See also Anger function; Weber function; Struve function.

Lommel functions were studied by E. Lommel [1].

References

[1] E. Lommel, "Zur Theorie der Bessel'schen Funktionen IV" Math. Ann. , 16 (1880) pp. 183–208
[2] G.N. Watson, "A treatise on the theory of Bessel functions" , 1 , Cambridge Univ. Press (1952)
[3] E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden" , 1. Gewöhnliche Differentialgleichungen , Chelsea, reprint (1947)
How to Cite This Entry:
Lommel function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lommel_function&oldid=31323
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article