Geodesic
A study on a class of q-Euler polynomials under the symmetric group of degree n
Araci, Serkan1 ; Duran, Ugur2 ; Acikgoz, Mehmet2
1 Department of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey
2 Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkey
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5196-5201.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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 $S_n$.
DOI : 10.22436/jnsa.009.08.05
Classification : 11B68, 05A19, 11S80, 05A30
Keywords: Symmetric identities, q-extension of \(\lambda\)-Euler polynomials, fermionic p-adic invariant integral on \(\mathbb{Z}_p\), invariant under \(S_n\).

Araci, Serkan 1 ; Duran, Ugur 2 ; Acikgoz, Mehmet 2

1 Department of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey
2 Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkey 
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Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet. A study on a class of q-Euler polynomials under the symmetric group of degree n. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5196-5201. doi : 10.22436/jnsa.009.08.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.08.05/

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[2] Duran, U.; Acikgoz, M.; Araci, S. Symmetric identities involving weighted q-Genocchi polynomials under \(S_4\), Proc. Jangjeon Math. Soc., Volume 18 (2015), pp. 455-465

[3] He, Y.; Araci, S. Sums of products of Apostol-Bernoulli and Apostol-Euler polynomials, Adv. Difference Equ., Volume 2014 (2014), pp. 1-13

[4] He, Y.; Araci, S.; Srivastava, H. M.; Acikgoz, M. Some new identities for the Apostol-Bernoulli polynomials and the Apostol-Genocchi polynomials, Appl. Math. Comput., Volume 262 (2015), pp. 31-41

[5] Kim, T. q-Volkenborn integration, Russ. J. Math. Phys.,, Volume 9 (2002), pp. 288-299

[6] Kim, T. Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on \(\mathbb{Z}_p\), Russ. J. Math. Phys., Volume 16 (2009), pp. 484-491

[7] Kim, T. Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on \(\mathbb{Z}_p\), Russ. J. Math. Phys., Volume 16 (2009), pp. 93-96

[8] Kim, D. S.; Kim, T. Some identities of symmetry for q-Bernoulli polynomials under symmetric group of degree n, Ars Combin., Volume 126 (2016), pp. 435-441

[9] Kim, T.; Kim, Y. H.; Hwang, K. W. On the q-extensions of the Bernoulli and Euler numbers, related identities and Lerch zeta function, Proc. Jangjeon Math. Soc., Volume 12 (2009), pp. 77-92

[10] Kim, T.; Kim, D. S.; Kwon, H. I.; Seo, J. J.; Dolgy, D. V. Some identities of q-Euler polynomials under the symmetric group of degree n, J. Nonlinear Sci. Appl., Volume 9 (2016), pp. 1077-1082

[11] Lu, D. Q.; Srivastava, H. M. Some series identities involving the generalized Apostol type and related polynomials, Comput. Math. Appl., Volume 62 (2011), pp. 3591-3602

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