Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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SOME PROPERTIES OF DEGENERATE q-POLY-TANGENT POLYNOMIALS

  • CHUNGHYUN YU (Department of Mathematics Education, Hannam University)
  • Received : 2022.12.28
  • Accepted : 2023.02.25
  • Published : 2023.03.30
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Abstract

In this paper, we give explicit identities for the degenerate q-poly-tangent numbers and polynomials. Finally, we obtain the relation of degenerate q-poly-tangent polynomials and Stirling numbers of the first kind and Stirling numbers of the second kind.

Keywords

Acknowledgement

The numerical computations and graph of the distribution of roots in this paper were assisted by Prof. C.S. Ryoo. We would like to thank Prof. C.S. Ryoo for his assistance.

References

  1. R.P. Agarwal and C.S. Ryoo, On degenerate poly-tangent numbers and polynomials and distribution of their zeros, J. Appl. & Pure Math. 1 (2019), 141-155.
  2. L.C. Andrews, Special Functions for Engineers and Applied Mathematicians, Macmillan Publishing Company, New York, 1985.
  3. G.E. Andrews, R. Askey, R. Roy, Special Functions, Cambridge University Press, Cambridge, 1999.
  4. K.N. Boyadzhiev, A series transformation formula and related polynomials, Internation Journal of Mathematics and Mathematical Sciences 2005:23 (2005), 3849-3866. https://doi.org/10.1155/IJMMS.2005.3849
  5. A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, Vol 3., Krieger, New York, 1981.
  6. C.S. Ryoo, R.P. Agarwal, Some identities involving q-poly-tangent numbers and polynomials and distribution of their zeros, Advances in Difference Equations 213 (2017). DOI 10.1186/s13662-017-1275-2
  7. C.S. Ryoo, A numerical investigation on the structure of the zeros of the degenerate Euler-tangent mixed-type polynomials, J. Nonlinear Sci. Appl. 10 (2017), 4474-4484. https://doi.org/10.22436/jnsa.010.08.39
  8. 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
  9. C.S. Ryoo, Notes on degenerate tangent polynomials, Global Journal of Pure and Applied Mathematics 11 (2015), 3631-3637.
  10. C.S. Ryoo, Some identities involving the generalized polynomials of derangements arising from differential equation, J. Appl. Math. & Informatics 38 (2020), 159-173.
  11. 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
  12. 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