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http://dx.doi.org/10.4134/BKMS.2014.51.3.831

A FURTHER INVESTIGATION OF GENERATING FUNCTIONS RELATED TO PAIRS OF INVERSE FUNCTIONS WITH APPLICATIONS TO GENERALIZED DEGENERATE BERNOULLI POLYNOMIALS  

Gaboury, Sebastien (Department of Mathematics and Computer Science University of Quebec at Chicoutimi)
Tremblay, Richard (Department of Mathematics and Computer Science University of Quebec at Chicoutimi)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.3, 2014 , pp. 831-845 More about this Journal
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$\grave{e}$ere [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$\ddot{o}$rlund polynomials;
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