# 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)
• Received : 2013.05.07
• Published : 2014.05.31
• 98 10

#### 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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