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

On some identities for confluent hypergeometric functions and Bessel functions