IJPAM: Volume 110, No. 2 (2016)

Title

SYMMETRIC IDENTITIES FOR CARLITZ-TYPE TWISTED
$(h,q)$-BERNOULLI NUMBERS AND POLYNOMIALS
ASSOCIATED WITH $p$-ADIC $q$-INTEGRAL ON $\mathbb{Z}_p$

Authors

C.S. Ryoo
Department of Mathematics
Hannam University
Daejeon, 306-791, KOREA

Abstract

In this paper, we obtain some interesting symmetric identities for Carlitz's twisted $(h,q)$-Bernoulli polynomials in $p$-adic field. Some interesting results and relationships are obtained.

History

Received: June 15, 2015
Revised: May 9, 2016
Published: November 5, 2016

AMS Classification, Key Words

AMS Subject Classification: 11B68, 11S40, 11S80
Key Words and Phrases: Bernoulli numbers and polynomials, $q$-Bernoulli numbers and polynomials, twisted $(h,q)$-Bernoulli numbers and polynomials, symmetric identity

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Bibliography

1
Yuan He, Symmetric identities for Carlitz's $q$-Bernoullinumbers and polynomials, Advances in Difference Equations, 246(2013), 10 pages.

2
T. Kim, $q$-Volkenborn integration, Russ. J. Math. Phys., 2002 (9), 288-299.D. Kim, T. Kim, S.-H. Lee, J.-J. Seo, A $p$-adic Approach toIdentities of Symmetry for Carlitz's $q$-Bernoulli Polynomials,Applied Mathemtical Sciences 8(14) (2014), 663-669.

3
B. A. Kupershmidt, Reflection symmetries of $q$-Bernoullipolynomials, J. Nonlinear Math. Phys., 12 (2005), 412-422.

4
C. S. Ryoo, Symmetric Identities for Carlitz's Twisted$q$-Bernoulli Polynomials Associated with $p$-Adic $q$-Integral on$\mathbb{Z}_p$, Applied Mathematical Sciences, 9(72) (2015), 3569 - 3575. Y. Simesk, V. Kurt, D. Kim, New approach to the complete sumof products of the twisted $(h,q)$-Bernoulli numbers andpolynomials, J. Nonlinear Math. Phys. 14 (2007), 44-56.

How to Cite?

DOI: 10.12732/ijpam.v110i2.13 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: 110
Issue: 2
Pages: 389 - 395


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