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FURTHER HYPERGEOMETRIC IDENTITIES DEDUCIBLE BY FRACTIONAL CALCULUS
Gaboury, Sebastien,Rathie, Arjun K. Korean Mathematical Society 2014 대한수학회논문집 Vol.29 No.3
Motivated by the recent investigations of several authors, in this paper we present a generalization of a result obtained recently by Choi et al. ([3]) involving hypergeometric identities. The result is obtained by suitably applying fractional calculus method to a generalization of the hypergeometric transformation formula due to Kummer.
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.
FURTHER EXPANSION AND SUMMATION FORMULAS INVOLVING THE HYPERHARMONIC FUNCTION
Gaboury, Sebastien Korean Mathematical Society 2014 대한수학회논문집 Vol.29 No.2
The aim of the paper is to present several new relationships involving the hyperharmonic function introduced by Mez$\ddot{o}$ in (I. Mez$\ddot{o}$, Analytic extension of hyperharmonic numbers, Online J. Anal. Comb. 4, 2009) which is an analytic extension of the hyperharmonic numbers. These relations are obtained by using some fractional calculus theorems as Leibniz rules and Taylor like series expansions.
EVALUATION OF A NEW CLASS OF DOUBLE DEFINITE INTEGRALS
Gaboury, Sebastien,Rathie, Arjun Kumar Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.4
Inspired by the results obtained by Brychkov ([2]), the authors evaluate a large number of new and interesting double definite integrals. The results are obtained with the use of classical hypergeometric summation theorems and a well-known double finite integral due to Edwards ([3]). The results are given in terms of Psi and Hurwitz zeta functions suitable for numerical computations.
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.
SYMMETRY PROPERTIES FOR A UNIFIED CLASS OF POLYNOMIALS ATTACHED TO χ
Gaboury, S.,Tremblay, R.,Fugere, J. The Korean Society for Computational and Applied M 2013 Journal of applied mathematics & informatics Vol.31 No.1
In this paper, we obtain some generalized symmetry identities involving a unified class of polynomials related to the generalized Bernoulli, Euler and Genocchi polynomials of higher-order attached to a Dirichlet character. In particular, we prove a relation between a generalized X version of the power sum polynomials and this unified class of 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.
S. Gaboury,R. Tremblay 장전수학회 2014 Proceedings of the Jangjeon mathematical society Vol.17 No.1
Application of a Taylor-like expansion theorem involving fractional derivatives to multivariable -function
Evaluation of a double integral
S. Gaboury,A. K. Rathie 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.3
Recently, Brychkov [Yu. A. Brychkov, Evaluation of some classes of definite and indefinite integrals, Integral Transforms Spec. Funct. 13 (2002), 163{167] evaluated some new classes of denite and inde nite single and double integrals involving various elementary special functions and the logarithmic function. The aim of this short note is to obtain an interesting double integral in terms of Psi and Hurwitz zeta functions suitable for numerical computations. A few special cases, including the one obtained by Brychkov, are also given.