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

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.

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.

Keywords

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

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