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.
Lommel functions were studied by E. Lommel .
|||E. Lommel, "Zur Theorie der Bessel'schen Funktionen IV" Math. Ann. , 16 (1880) pp. 183–208|
|||G.N. Watson, "A treatise on the theory of Bessel functions" , 1 , Cambridge Univ. Press (1952)|
|||E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden" , 1. Gewöhnliche Differentialgleichungen , Chelsea, reprint (1947)|
Lommel function. E.D. Solomentsev (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Lommel_function&oldid=12539