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Certain hypergeometric series identities deducible by fractional calculus
S. Gaboury,A. K. Rathie 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.2
Motivated by the recent investigations of several authors, in this paper we present a generalization of a result obtained recently by Ibrahim et al. (A. K. Ibrahim, M. A. Rakha and A. K. Rathie, On certain hypergeometric identities deducible by using the beta integral method, Adv. Dierence Equ. 2013: 341 (2013), 1-8) involving hypergeometric identities. The result is obtained by suitably applying fractional calculus method to a generalization of a quadratic transformation for the Gauss hypergeometric function due to Kummer.
S. Gaboury,A. Bayad 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.2
The aim of this paper is to make use of a new generalized Leibniz rule for fractional derivatives obtained recently by Tremblay et al. [Tremblay, Gaboury and Fugere, A new Leibniz rule and its integral analogue for fractional derivatives, Integral Transforms Spec. Funct. 24 (2013), 111-128] by means of a representation based on the Pochhammer's contour of integration for fractional derivatives in order to derive new expansion formulas for several families of the Hurwitz- Lerch zeta function. Special cases are also given.
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.
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.
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,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
Some explicit formulas for certain new classes of Bernoulli, Euler and Genocchi polynomials
S. Gaboury,R. Tremblay,B-J Fugere 장전수학회 2014 Proceedings of the Jangjeon mathematical society Vol.17 No.1
Some explicit formulas for certain new classes of Bernoulli, Euler and Genocchi polynomials
A FURTHER GENERALIZATION OF APOSTOL-BERNOULLI POLYNOMIALS AND RELATED POLYNOMIALS
Tremblay, R.,Gaboury, S.,Fugere, J. The Honam Mathematical Society 2012 호남수학학술지 Vol.34 No.3
The purpose of this paper is to introduce and investigate two new classes of generalized Bernoulli and Apostol-Bernoulli polynomials based on the definition given recently by the authors [29]. In particular, we obtain a new addition formula for the new class of the generalized Bernoulli polynomials. We also give an extension and some analogues of the Srivastava-Pint$\acute{e}$r addition theorem [28] for both classes. Finally, by making use of the new adition formula, we exhibit several interesting relationships between generalized Bernoulli polynomials and other polynomials or special functions.