DOI QR코드

DOI QR Code

SYMMETRIC IDENTITIES FOR DEGENERATE q-POLY-BERNOULLI NUMBERS AND POLYNOMIALS

  • JUNG, N.S. (College of Talmage Liberal Arts, Hannam University) ;
  • RYOO, C.S. (Department of Mathematics, Hannam University)
  • Received : 2017.05.23
  • Accepted : 2017.09.15
  • Published : 2018.01.30

Abstract

In this paper, we introduce a degenerate q-poly-Bernoulli numbers and polynomials include q-logarithm function. We derive some relations with this polynomials and the Stirling numbers of second kind and investigate some symmetric identities using special functions that are involving this polynomials.

Keywords

References

  1. T. Arakawa and M. Kaneko, On Poly-Bernoulli numbers, Comment. Math. Univ. Sanct. Pauli 48-2 (1999), 159167.
  2. A. Bayad and Y. Hamahata, Polylogarithms and poly-Bernoulli polynomials, Kyushu. J. Math. 65 (2011), 15-24. https://doi.org/10.2206/kyushujm.65.15
  3. Mehmet Cenkcia, Takao Komatsub, Poly-Bernoulli numbers and polynomials with a q parameter, Journal of Number Theory 152(2015), 38-54. https://doi.org/10.1016/j.jnt.2014.12.004
  4. L. Carlitz, Degenerate stirling Bernoulli and Eulerian numbers, Util. Math 15(1979), 51-88.
  5. L. Carlitz, Weighted Stirling numbers of the first kind and second kind - I, Fibonacci Quart 18(1980), 147-162.
  6. K.W.Hwang, B.R. Nam, N.S. Jung, A note on q-analogue of poly-Bernoulli numbers and polynomials, J. Appl. Math. & Informatics 35(2017), 677-621.
  7. Waseem A. Khan, A note on degenerate hermite poly-Bernoulli numbers and polynomials, Journal of Classical Analysis 8(1)(2016), 65-76. https://doi.org/10.7153/jca-08-06
  8. M.Kaneko, Poly-Bernoulli numbers, Journal de thorie des nombres de Bordeaux 9(1997), 221-228.
  9. Dae San Kim, Taekyun Kim, A note on degenerate poly-Bernoulli numbers and polynomials, Advances in Difference Equation 2015:258(2015).
  10. C.S. Ryoo, A Note on the Zeros of the q-Bernoulli Polynomials, J. Appl. Math. & Informatics 28 (2010), 805-811.
  11. C.S. Ryoo, Re ection Symmetries of the q-Genocchi Polynomials, J. Appl. Math. & Informatics 28 (2010), 1277-1284.
  12. C.S. Ryoo, On degenerate numbers and polynomials related to the Stirling numbers and Bell polynomials, Global Journal of pure and applied mathematics 12(4)(2016), 3407-3413.
  13. C.S. Ryoo, R.P. Agarwal, Some identities involving q-poly-tangent numbers and polynomials and distribution of their zeros, Advances in Difference Equations 2017:213(2017), 1-14.
  14. Paul Thomas Young, Degenerate Bernoulli polynomials, generalized factorial sums, and their applications, Journal of Number Theory 128 (2008), 738-758. https://doi.org/10.1016/j.jnt.2007.02.007

Cited by

  1. SOME PROPERTIES OF DEGENERATE CARLITZ-TYPE TWISTED q-EULER NUMBERS AND POLYNOMIALS vol.39, pp.1, 2018, https://doi.org/10.14317/jami.2021.001