Journal of Applied and Pure Mathematics

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

DOI QR Code

DISTRIBUTION OF ZEROS OF THE COSINE-TANGENT AND SINE-TANGENT POLYNOMIALS

  • CHA, K.H. (Department of Mathematics, Hannam University) ;
  • LEE, H.Y. (Department of Mathematics, Hannam University)
  • Received : 2022.02.17
  • Accepted : 2022.05.20
  • Published : 2022.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we give some interesting properties of the cosine tangent polynomials and sine tangent polynomials. In addition, we give some identities for these polynomials and the distribution of zeros of these polynomials.

Keywords

Acknowledgement

The graph of the distribution of roots in this paper was assisted by Professor Ryoo. We would like to express our gratitude to Professor Ryoo for his help.

References

  1. G.E. Andrews, R. Askey, R. Roy, Special Functions, Vol. 71, Combridge Press, Cambridge, UK, 1999.
  2. R. Ayoub, Euler and zeta function, Amer. Math. Monthly 81 (1974), 1067-1086. https://doi.org/10.1080/00029890.1974.11993738
  3. L. Comtet, Advances Combinatorics, Riedel, Dordrecht, 1974.
  4. T. Kim, C.S. Ryoo Some identities for Euler and Bernoulli polynomials and their zeros, Axioms 2018 (2018), doi:10.3390/axioms7030056.
  5. M.J. Park and J.Y. Kang, A study on the cosine tangent polynomials and sine tangent polynomials, J. Appl. & Pure Math. 2 (2020), 47-56.
  6. C.S. Ryoo, A note on the tangent numbers and polynomials, Adv. Studies Theor. Phys. 7 (2013), 447-454. https://doi.org/10.12988/astp.2013.13042
  7. C.S. Ryoo, A numerical investigation on the zeros of the tangent polynomials, J. App. Math. & Informatics 32 (2014), 315-322. https://doi.org/10.14317/JAMI.2014.315
  8. C.S. Ryoo, Modified degenerate tangent numbers and polynomials, Global Journal of Pure and Applied Mathematics 12 (2016), 1567-1574.
  9. H. Shin, J. Zeng, The q-tangent and q-secant numbers via continued fractions, European J. Combin. 31 (2010), 1689-1705. https://doi.org/10.1016/j.ejc.2010.04.003
  10. P.T. Young, Degenerate Bernoulli polynomials, generalized factorial sums, and their applications, Journal of Number Theorey 128 (2008), 738-758. https://doi.org/10.1016/j.jnt.2007.02.007