Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME PROPERTIES OF DEGENERATE CARLITZ-TYPE TWISTED q-EULER NUMBERS AND POLYNOMIALS

  • Received : 2020.10.28
  • Accepted : 2020.12.17
  • Published : 2021.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we define degenerate Carlitz-type twisted q-Euler numbers and polynomials by generalizing the degenerate Euler numbers and polynomials, Carlitz's type degenerate q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, symmetric properties, a connection with degenerate Carlitz-type twisted q-Euler numbers and polynomials.

Keywords

References

  1. R.P. Agarwal and C.S. Ryoo, Differential equations associated with generalized Truesdell polynomials and distribution of their zeros, J. Appl. & Pure Math. 1 (2019), 11-24.
  2. F.T. Howard, Degenerate weighted Stirling numbers, Discrete Mathematics 57 (1985), 45-58. https://doi.org/10.1016/0012-365X(85)90155-4
  3. F.T. Howard, Explicit formulas for degenerate Bernoulli numbers, Discrete Mathematics 162 (1996), 175-185. https://doi.org/10.1016/0012-365X(95)00284-4
  4. K.W. Hwang, C.S. Ryoo, Some symmetric identities for degenerate Carlitz-type (p, q)-Euler numbers and polynomials, Symmetry 11 (2019), doi:10.3390/sym11060830.
  5. N.S. Jung, C.S. Ryoo, Symmetric identities for degenerate q-poly-Bernoulli numbers and polynomials, J. Appl. Math. & Informatics 36 (2018), 29-38. https://doi.org/10.14317/jami.2018.029
  6. J.Y. Kang, A study on q-special numbers and polynomials with q-exponential distribution, J. Appl. Math. & Informatics 36 (2018), 541-553. https://doi.org/10.14317/JAMI.2018.541
  7. M.S. Kim, On p-adic Euler L-function of two variables, J. Appl. Math. & Informatics 36 (2018), 369-379. https://doi.org/10.14317/JAMI.2018.369
  8. F. Qi, D.V. Dolgy, T. Kim, C.S. Ryoo, On the partially degenerate Bernoulli polynomials of the first kind, Global Journal of Pure and Applied Mathematics 11 (2015), 2407-2412.
  9. C.S. Ryoo, On degenerate Carlitz-type (h, q)-tangent numbers and polynomials, Journal of Algebra and Applied Mathematics 16 (2018), 119-130.
  10. C.S. Ryoo, Some identities for (p, q)-Hurwitz zeta function, J. Appl. Math. & Informatics 37 (2019), 97-103. https://doi.org/10.14317/JAMI.2019.097
  11. C.S. Ryoo, Differential equations associated with twisted (h, q)-tangent polynomials, J. Appl. Math. & Informatics 36 (2018), 205-212. https://doi.org/10.14317/JAMI.2018.205
  12. C.S. Ryoo, Symmetric identities for degenerate Carlitz-type q-Euler numbers and polynomial , J. Appl. Math. & Informatics 37 (2019), 97-103. https://doi.org/10.14317/JAMI.2019.097
  13. C.S. Ryoo, Some properties of the (h, q)-Euler numbers and polynomials and computation of their zeros, J. Appl. & Pure Math. 1 (2019), 1-10.
  14. C.S. Ryoo, Some symmetric identities for (p, q)-Euler zeta function, Journal of Computational Analysis and Applications 27 (2019), 361-366.
  15. C.S. Ryoo, Symmetric identities for the second kind q-Bernoulli polynomials, Journal of Computational Analysis and Applications 28 (2020), 654-659.
  16. C.S. Ryoo, Symmetric identities for Dirichlet-type multiple twisted (h, q)-l-function and higher-order generalized twisted (h, q)-Euler polynomials, Journal of Computational Analysis and Applications 28 (2020), 537-542.
  17. C.S. Ryoo, Symmetric identities for degenerate Carlitz-type q-Euler numbers and polynomial, J. Appl. Math. & Informatics 37 (2019), 97-103 . https://doi.org/10.14317/JAMI.2019.097
  18. C.S. Ryoo, On the Carlitz's type twisted (p, q)-Euler polynomials and twisted (p, q)-Euler zeta function, Journal of Computational Analysis and Applications 29 (2021), 582-587.
  19. C.S. Ryoo, Some properties of the (h, p, q)-Euler numbers and polynomials and computation of their zeros, J. Appl. & Pure Math. 1 (2019), 1-10.
  20. P.T. 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