On the representation of cylinder functions

Abstract

In this paper, we present a mixed-type integral-sum representation of the cylinder functions ${\mathcal{C}}_{\mu }(z)$, which holds for unrestricted complex values of the order $\mu$ and for any complex value of the variable $z$. Particular cases of these representations and some applications, which include the discussion of limiting forms and representations of related functions, are also discussed.

17 pages