Integral Representations of Bargmann Type for the β-Modified Bergman Space on Punctured Unit Disc

We deal with the integral representation of Bargmann type of the functions belonging to the β -modified Bergman space on the punctured unit disc, by means of some special kernel-distribution involving the confluent hypergeometric functions and generalizing the classical second Bargmann transform. As application, we derive integral formula on the unit disc for the product of confluent hypergeometric functions, by considering the associated fractional Hankel transform.