Bulletin of the
Korean Mathematical Society BKMS

In this paper, we obtain new generating functions involving families of pairs of inverse functions by using a generalization of the Srivastava's theorem [H. M. Srivastava, Some generalizations of Carlitz's theorem, Pacific J. Math. 85 (1979), 471--477] obtained by Tremblay and Fug\`{e}re [Generating functions related to pairs of inverse functions, Transform methods and special functions, Varna '96, Bulgarian Acad. Sci., Sofia (1998), 484--495]. Special cases are given. These can be seen as generalizations of the generalized Bernoulli polynomials and the generalized degenerate Bernoulli polynomials.

Keywords: generating functions, multiparameter and multivariate generating functions, inverse functions, Bernoulli polynomials, N\"{o}rlund polynomials

MSC numbers: 11B68, 33A65, 33A70, 26A33, 33E15