Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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EXPLICIT IDENTITIES INVOLVING GEOMETRIC POLYNOMIALS ARISING FROM DIFFERENTIAL EQUATIONS AND THEIR ZEROS

  • KANG, J.Y. (Department of Mathematics Education, Silla University) ;
  • RYOO, C.S. (Department of Mathematics, Hannam University)
  • Received : 2021.12.13
  • Accepted : 2022.04.30
  • Published : 2022.05.30
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Abstract

In this paper, we study differential equations arising from the generating functions of the geometric polynomials. We give explicit identities for the geometric polynomials. Finally, we investigate the zeros of the geometric polynomials by using computer.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (No. 2017R1A2B4006092).

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. 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, England, 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, McGraw-Hill Book Company, INC., Vol 3. New York, Krieger, 1981.
  6. K.W. Hwang, C.S. Ryoo, N.S. Jung, Differential equations arising from the generating function of the (r, β)-Bell polynomials and distribution of zeros of equations, Mathematics 7 (2019), doi:10.3390/math7080736.
  7. J.Y. Kang, H.Y. Lee, N.S. Jung, Some relations of the twisted q-Genocchi numbers and polynomials with weight α and weak Weight β, Abstract and Applied Analysis 2012 (2012), 1-9. https://doi.org/10.1155/2012/153456
  8. M.S. Kim, S. Hu, On p-adic Hurwitz-type Euler Zeta functions, J. Number Theory 132 (2012), 2977-3015. https://doi.org/10.1016/j.jnt.2012.05.037
  9. T. Kim, D.S. Kim, Identities involving degenerate Euler numbers and polynomials arising from non-linear differential equations, J. Nonlinear Sci. Appl. 9 (2016), 2086-2098. https://doi.org/10.22436/jnsa.009.05.14
  10. G. Liu, Congruences for higher-order Euler numbers, Proc. Japan Acad. 82A (2009), 30-33.
  11. N. Privault, Genrealized Bell polynomials and the combinatorics of Poisson central moments, The Electronic Journal of Combinatorics 18 (2011), # 54.
  12. A.M. Robert, A Course in p-adic Analysis, Graduate Text in Mathematics, Vol. 198, Springer, 2000.
  13. C.S. Ryoo, A numerical investigation on the structure of the zeros of the degenerate Eulertangent mixed-type polynomials, J. Nonlinear Sci. Appl. 10 (2017), 4474-4484. https://doi.org/10.22436/jnsa.010.08.39
  14. C.S. Ryoo, Differential equations associated with generalized Bell polynomials and their zeros, Open Mathematics 14 (2016), 807-815. https://doi.org/10.1515/math-2016-0075
  15. C.S. Ryoo, R.P. Agarwal, J.Y. Kang, Differential equations associated with Bell-Carlitz polynomials and their zeros, Neural Parallel Sci. Comput. 24 (2016), 453-462.
  16. C.S. Ryoo, Differential equations associated with tangent numbers, J. Appl. Math. & Informatics 34 (2016), 487-494. https://doi.org/10.14317/JAMI.2016.487
  17. C.S. Ryoo, Some identities involving the generalized polynomials of derangements arising from differential equation, J. Appl. Math. & Informatics 38 (2020), 159-173. https://doi.org/10.14317/jami.2020.159
  18. Y. Simsek, Complete Sum of Products of (h, q)-Extension of Euler Polynomials and Numbers, Journal of Difference Equations and Applications 16 (2010), 1331-1348. https://doi.org/10.1080/10236190902813967