# 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
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.

### Share and Cite

##### ISRP Style

Serkan Araci, Mehmet Acikgoz, Toka Diagana, H. M. Srivastava, A novel approach for obtaining new identities for the lambda extension of q-Euler polynomials arising from the q-umbral calculus, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1316--1325

##### AMA Style

Araci Serkan, Acikgoz Mehmet, Diagana Toka, Srivastava H. M., A novel approach for obtaining new identities for the lambda extension of q-Euler polynomials arising from the q-umbral calculus. J. Nonlinear Sci. Appl. (2017); 10(4):1316--1325

##### Chicago/Turabian Style

Araci, Serkan, Acikgoz, Mehmet, Diagana, Toka, Srivastava, H. M.. "A novel approach for obtaining new identities for the lambda extension of q-Euler polynomials arising from the q-umbral calculus." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1316--1325

### Keywords

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

•  11B68
•  11S80
•  11B65
•  33D15

### References

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