A further investigation of generating functions related to pairs of inverse functions with applications to generalized degenerate Bernoulli polynomials
Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 831-845
https://doi.org/10.4134/BKMS.2014.51.3.831
Published online May 31, 2014
Sebastien Gaboury and Richard Tremblay
University of Quebec at Chicoutimi, University of Quebec at Chicoutimi
Abstract : 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
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