DOI QR코드

DOI QR Code

DEGENERATE POLYEXPONENTIAL FUNCTIONS AND POLY-EULER POLYNOMIALS

  • Kurt, Burak (Mathematics of Department Education Faculty Akdeniz University)
  • 투고 : 2020.05.18
  • 심사 : 2020.06.26
  • 발행 : 2021.01.31

초록

Degenerate versions of the special polynomials and numbers since they have many applications in analytic number theory, combinatorial analysis and p-adic analysis. In this paper, we define the degenerate poly-Euler numbers and polynomials arising from the modified polyexponential functions. We derive explicit relations for these numbers and polynomials. Also, we obtain some identities involving these polynomials and some other special numbers and polynomials.

키워드

참고문헌

  1. N. K. Boyadzhiev, Polyexponentials, arxiv:07710.1330 [Math. NT].
  2. L. Carlitz, A note on Bernoulli and Euler polynomials of the second kind, Scripta Math. 25 (1961), 323-330.
  3. L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math. 15 (1979), 51-88.
  4. U. Duran and M. Acikgoz, On the degenerate Gould-Hopper based full degenerate Bell polynomials, J. Math. Comp. Sci. 21 (2020), 243-257. https://doi.org/10.22436/jmcs.021.03.07
  5. D. S. Kim and T. Kim, Higher order degenerate Euler polynomials, App. Math. Sci. 9 (2015), no. 2, 57-73.
  6. D. S. Kim and T. Kim, A note on polyexponential and unipoly functions, Russ. J. Math. Phys. 26 (2019), no. 1, 40-49. https://doi.org/10.1134/S1061920819010047
  7. D. S. Kim and T. Kim, A note on a new type of degenerate Bernoulli numbers, Russ. J. Math. Phys. 27 (2020), no. 2, 227-235. https://doi.org/10.1134/S1061920820020090
  8. T. Kim and D. S. Kim, Degenerate polyexponential functions and degenerate Bell polynomials, J. Math. Anal. Appl. 487 (2020), no. 2, 124017, 15 pp. https://doi.org/10.1016/j.jmaa.2020.124017
  9. T. Kim, D. S. Kim, L. Jang, and H. Lee, Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae-Stirling numbers, Adv. Difference Equ. 2020 (2020), Paper No. 245, 19 pp. https://doi.org/10.1186/s13662-020-02701-1
  10. T. Kim, D. S. Kim, H. Y. Kim, and L.-C. Jang, Degenerate poly-Bernoulli numbers and polynomials, Informatica 31 (2020), 2-8.
  11. T. Kim, D. S. Kim, Y. H. Kim, and J. Kwon, Degenerate Stirling polynomials of the second kind and some applications, Symmetry 11.1046 (2019), 1-11. https://doi.org/10.3390/sym11010001
  12. T. Kim, D. S. Kim, J. Kwon, and H. Y. Kim, A note on degenerate Genocchi and polyGenocchi numbers and polynomials, J. Inequal. Appl. 2020 (2020), Paper No. 110, 13 pp. https://doi.org/10.1186/s13660-020-02378-w
  13. T. Kim, D. S. Kim, J. Kwon, and H. Lee, Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials, Adv. Difference Equ. 2020 (2020), Paper No. 168, 12 pp. https://doi.org/10.1186/s13662-020-02636-7
  14. D. Lim, Some identities of degenerate Genocchi polynomials, Bull. Korean Math. Soc. 53 (2016), no. 2, 569-579. https://doi.org/10.4134/BKMS.2016.53.2.569
  15. H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, Inc., Amsterdam, 2012. https://doi.org/10.1016/B978-0-12-385218-2.00001-3