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Gaboury, Sebastien,Tremblay, Richard Korean Mathematical Society 2014 대한수학회보 Vol.51 No.3
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.
Sebastien Gaboury,Richard Tremblay 대한수학회 2014 대한수학회보 Vol.51 No.3
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`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.
S. Gaboury,Richard Tremblay 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.2
The aim of this present paper is to present a general expan-sion theorem involving H-functions of several complex variables. This is done by making use of a Taylor-like expansion in terms of a quadratic function obtained by means of fractional derivatives given recently by one of the author. Special cases are computed to illustrate interesting presumably new expansions.
Gaboury, Sebastien,Ozarslan, Mehmet Ali,Tremblay, Richard Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.4
Recently, Liu et al. [Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella function, Integral Transform Spec. Funct. 23 (2012), no. 7, 539-549] investigated, in several interesting papers, some various families of bilateral generating functions involving the Chan-Chyan-Srivastava polynomials. The aim of this present paper is to obtain some bilateral generating functions involving the Chan-Chyan-Sriavastava polynomials and three general classes of multivariable polynomials introduced earlier by Srivastava in [A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), 1-6], [A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 117 (1985), 183-191] and by Kaano$\breve{g}$lu and $\ddot{O}$zarslan in [Two-sided generating functions for certain class of r-variable polynomials, Mathematical and Computer Modelling 54 (2011), 625-631]. Special cases involving the (Srivastava-Daoust) generalized Lauricella functions are also given.