A novel approach for obtaining new identities for the lambda extension of q-Euler polynomials arising from the q-umbral calculus

Volume 10, Issue 4, pp 1316--1325 http://dx.doi.org/10.22436/jnsa.010.04.03

Publication Date: April 20, 2017 Submission Date: September 30, 2016

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Authors

Serkan Araci - Department of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey. Mehmet Acikgoz - Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, TR-27310 Gaziantep, Turkey. Toka Diagana - Department of Mathematics, Howard University, 2441 6th Street, NW Washington 20059, D.C., U.S.A. H. M. Srivastava - Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada. - China Medical University, Taichung 40402, Taiwan, Republic of China.

Abstract

In this article, a new q-generalization of the Apostol-Euler polynomials is introduced using the usual q-exponential function. We make use of such a generalization to derive several properties arising from the q-umbral calculus.

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Keywords

• \(q\)-Apostol-Euler polynomials
• \(q\)-numbers
• \(q\)-exponential function
• \(q\)-umbral calculus
• (\(\lambda،q\))-Euler numbers
• (\(\lambda،q\))-Euler polynomials
• properties and identities.

MSC

•  11B68
•  11S80
•  11B65
•  33D15

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