Title: Indefinite Integrals of Spherical Bessel Functions,
Abstract: 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.