IJPAM: Volume 109, No. 3 (2016)

NOVEL IDENTITIES OF SYMMETRY FOR CARLITZ'S
TWISTED $q$-BERNOULLI POLYNOMIALS UNDER $S_{4}$

Ugur Duran$^1$, Mehmet Acikgoz$^2$
$^{1,2}$Department of Mathematics
Faculty of Arts and Science
University of Gaziantep
TR-27310 Gaziantep, TURKEY

Abstract. In this paper, the authors discover some new symmetric identities of Carlitz's twisted $q$-Bernoulli polynomials arising from the $p$-adic $q$-integral on $\mathbb{Z}_{p}$ under symmetric group of degree four shown by $S_{4}$.

Received: Febrauray 4, 2016

Revised: August 16, 2016

Published: October 1, 2016

AMS Subject Classification: 11S80, 11B68, 05A19, 05A30

Key Words and Phrases: symmetric identities, Carlitz's twisted $q$-Bernoulli polynomials, $p$-adic $q$-integral on $\mathbb{Z}_{p}$, invariant under $S_{4}$
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Bibliography

1
M. Acikgoz, S. Araci, U. Duran, New extensions of some known special polynomials under the theory of multiple q-calculus, Turkish Journal of Analysis and Number Theory, Vol. 3, No. 5, (2015

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DOI: 10.12732/ijpam.v109i3.15 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 3
Pages: 673 - 680


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