  Recently renewed interest in the Lobachevsky-type integrals and interesting
identities involving the cardinal sine motivate an extension of the classical
Parseval formula involving both periodic and non-periodic functions. We develop
a version of the Parseval formula that is often more practical in applications
and illustrate its use by extending recent results on Lobachevsky-type
integrals. Some previously known, interesting identities are re-proved in a
more transparent manner and new formulas for integrals involving cardinal sine
and Bessel functions are given.
