In this paper, we derive a new contour integral representation for the confluent hypergeometric function as well as for its various special cases. Consequently, we derive expansions of the confluent hypergeometric function in terms of functions of the same kind. Furthermore, we obtain a new identity involving integrals and sums of confluent hypergeometric functions. Our results generalized several well-known results in the literature.
- Received May 29, 2016.
- Accepted August 1, 2016.
- © 2016 The Author(s)
Published by the Royal Society. All rights reserved.