A study on a class of q-Euler polynomials under the symmetric group of degree n


Authors

Serkan Araci - Department of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey. Ugur Duran - Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkey. Mehmet Acikgoz - Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkey.


Abstract

Motivated by the paper of Kim et al. [T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, D. V. Dolgy, J. Nonlinear Sci. Appl., 9 (2016), 1077-1082], we study a class of q-Euler polynomials earlier given by Kim et al. in [T. Kim, Y. H. Kim, K. W. Hwang, Proc. Jangjeon Math. Soc., 12 (2009), 77-92]. We derive some new symmetric identities for q-extension of \(\lambda\)-Euler polynomials, using fermionic p-adic invariant integral over the p-adic number field originally introduced by Kim in [T. Kim, Russ. J. Math. Phys., 16 (2009), 484-491], under symmetric group of degree n denoted by \(S_n\).


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