On some identities for confluent hypergeometric functions and Bessel functions

Abstract: Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a foundation of current science. In this paper, we find a new integral representation of the Whittaker function of the first kind and show a relevant summation formula for Kummer's confluent hypergeometric functions. We also perform the specifications of our identities to link to known and new results.