Indefinite Integrals of Spherical Bessel Functions

Autor:	Bloomfield, Jolyon K., Face, Stephen H. P., Moss, Zander
Rok vydání:	2017
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	Highly oscillatory integrals, such as those involving Bessel functions, are best evaluated analytically as much as possible, as numerical errors can be difficult to control. We investigate indefinite integrals involving monomials in $x$ multiplying one or two spherical Bessel functions of the first kind $j_l(x)$ with integer order $l$. Closed-form solutions are presented where possible, and recursion relations are developed that are guaranteed to reduce all integrals in this class to closed-form solutions. These results allow for definite integrals over spherical Bessel functions to be computed quickly and accurately. For completeness, we also present our results in terms of ordinary Bessel functions, but in general, the recursion relations do not terminate. Comment: 12 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.06428 Zobrazit plný text záznamu View this record from Arxiv