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

Title & Authors
A FURTHER INVESTIGATION OF GENERATING FUNCTIONS RELATED TO PAIRS OF INVERSE FUNCTIONS WITH APPLICATIONS TO GENERALIZED DEGENERATE BERNOULLI POLYNOMIALS
Gaboury, Sebastien; Tremblay, Richard;

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$\small{\grave{e}}$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$\small{\ddot{o}}$rlund polynomials;
Language
English
Cited by
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