Journal of applied mathematics & informatics

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

DOI QR Code

NOTES ON THE PARAMETRIC POLY-TANGENT POLYNOMIALS

  • KURT, BURAK (Akdeniz University, Mathematics of Department)
  • Received : 2020.01.16
  • Accepted : 2020.05.07
  • Published : 2020.05.30
Download PDF
⟨ Previous Next ⟩

Abstract

Recently, M. Masjed-Jamai et al. in ([6]-[7]) and Srivastava et al. in ([15]-[16]) considered the parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. They proved some theorems and gave some identities and relations for these polynomials. In this work, we define the parametric poly-tangent numbers and polynomials. We give some relations and identities for the parametric poly-tangent polynomials.

Keywords

References

  1. Y. Hamahata, Poly-Euler polynomials and Arakawa-Kaneko type zeta function, Functiones et Approximation Commentari Math. 51 (2014), 7-22. https://doi.org/10.7169/facm/2014.51.1.1
  2. T. Kim, V.S. Sang and J.J. Seo, A note on poly-Genocchi numbers and polynomials, Appl. Math. Sci. 8 (2014), 4775-4781.
  3. D. Kim and T. Kim, A note on poly-Bernoulli and higher order poly-Bernoulli polynomials, Russion J. of Math. Physics 22 (2015), 26-33. https://doi.org/10.1134/S1061920815010057
  4. B. Kurt, Identities and relation on the Hermite-based tangent polynomials, TWMS Journal of Applied and Engineering Mathematics 2020, accepted.
  5. M.Q. Luo, The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of order, Integral Trans. Spec. Func. 20 (2009), 337-391.
  6. M. Masjed-Jamai and W. Koeff, Symbolic computation of some power-trigonometric series, J. of Symbolic Computation 80 (2017), 273-284. https://doi.org/10.1016/j.jsc.2016.03.004
  7. M. Masjed-Jamai, M.R. Beyki and W. Koepf, A new type of Euler polynomials and numbers, Mediterr. J. Math. 15 (2018).
  8. C.S. Ryoo, A note on the tangent numbers and polynomials, Adv. Stud. Theo. Phys. 7 (2013), 447-454. https://doi.org/10.12988/astp.2013.13042
  9. C.S. Ryoo, On degenerate Carlitz's type q-tangent numbers and polynomials associated with p-adic integral on $\mathbb{Z}_p$, App. Math. Sci. 11 (2017), 2367-2375. https://doi.org/10.12988/ams.2017.78257
  10. C.S. Ryoo and R.P. Agarwal, Some identities involving q-poly-tangent numbers and polynomials and distribution of zeros, Advances in Diff. Equa. 213 (2017), https://doi.org/10.1186/s13662-017-1275-2.
  11. C.S. Ryoo, A numerical investigation on the zeros of the tangent polynomials, J. Appl. Math. and Inform. 32 (2014), 315-322. https://doi.org/10.14317/jami.2014.315
  12. C.S. Ryoo, On the poly-tangent numbers and polynomials and distribution of their zeros, Global J. of Pure and Appl. Math. 12 (2016), 4411-5525.
  13. H.M. Srivastava and J. Choi, Zeta and q-zeta function and associated series and integral, Elsevier, Amsterdam, 2010.
  14. H.M. Srivastava, M. Garg and S. Choudhary, A new generalization of the Bernoulli and related polynomials, J. Math. Phys. 17 (2010), 251-261.
  15. H.M. Srivastava, M. Masjed-Jamai and M.R. Beyki, A parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, App. Math. Inf. Sci. 12 (2018), 907-916. https://doi.org/10.18576/amis/120502
  16. H.M. Srivastava and C. Kiziltas, A parametric kind of the Fubini-type polynomials, RAC-SAM 113 (2019), 3253-3267.