Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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SYMMETRIC PROPERTIES OF CARLITZ'S TYPE (p, q)-GENOCCHI POLYNOMIALS

  • KIM, A HYUN (Department of Mathematics, Hannam University)
  • Received : 2018.06.28
  • Accepted : 2019.03.25
  • Published : 2019.05.30
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Abstract

This paper defines Carlitz's type (p, q)-Genocchi polynomials and Carlitz's type (h, p, q)-Genocchi polynomials, and explains fourteen properties which can be complemented by Carlitz's type (p, q)-Genocchi polynomials and Carlitz's type (h, p, q)-Genocchi polynomials, including distribution relation, symmetric property, and property of complement. Also, it explores alternating powers sums by proving symmetric property related to Carlitz's type (p, q)-Genocchi polynomials.

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References

  1. Y. He, Symmetric identities for Carlitz's q-Bernoulli numbers and polynomials, Advances in Difference Equations (2013).
  2. J.Y. Kang, C.S. Ryoo, Symmetric identities for Carlitz's type twisted q-Genocchi polynomials using twisted q-Genocchi Zeta function, Applied Mathematical Sciences 8 (2014), 4405-4412. https://doi.org/10.12988/ams.2014.46509
  3. T. Kim, A note on the q-Genocchi numbers and polynomials, Journal of Inequalities and Applications (2007), 8 pages.
  4. T. Kim, On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl. 326 (2007), 1458-1465. https://doi.org/10.1016/j.jmaa.2006.03.037
  5. C.S. Ryoo, J.Y. Kang, A note on the q-Genocchi numbers and polynomials with weak weight ${\alpha}$, Applied Mathematical Sciences 6 (2012), 731-738.
  6. C.S. Ryoo, (p; q)-analogue of Euler Zeta function, J. Appl. Math. & Informatics 35 (2017), 113-120. https://doi.org/10.14317/jami.2017.113
  7. C.S. Ryoo, Some symmetric identities for (p; q)-Euler Zeta function, J. Computational Analysis and Applications 27 (2019), 361-366.