CALCULATING ZEROS OF THE GENERALIZED GENOCCHI POLYNOMIALS

  • Agarwal, R.P. (Department of Mathematical Sciences, Florida Institute of Technology) ;
  • Ryoo, C.S. (Department of Mathematics, Hannam University)
  • Published : 2009.05.31

Abstract

Kim [4] defined the generalized Genocchi numbers $G_{n,x}$. In this paper, we introduce the generalized Genocchi polynomials $G_{n,x}(x)$. One purpose of this paper is to investigate the zeros of the generalized Genocchi polynomials $G_{n,x}(x)$. We also display the shape of generalized Genocchi polynomials $G_{n,x}(x)$.

Keywords

References

  1. D. Dumont, Interpretations combinatoires des nombres de Genocchi , Duke Math. J. 41 (1974), 305-318. https://doi.org/10.1215/S0012-7094-74-04134-9
  2. R. Ehrenborg, E. Steingrimsson, Yet another triangle for the Genocchi numbers, Europ. J. Combin. 21 (2000), 593-600. https://doi.org/10.1006/eujc.1999.0370
  3. G. Kreweras, An Additive Generation for the Genocchi Numbers and Two of its Enumer- ative Meanings, Bull. Inst. Combin. Appl. 20 (1997), 99-103.
  4. T. Kim, L.-C. Jang, H. K. Pak, A note on q-Euler and Genocchi numbers , Proc. Japan Acad. 77 A (2001), 139-141.
  5. C.S.Ryoo, A numerical computation on the structure of the roots of q-extension of Genocchi polynomials, Applied Mathematics Letters 21 (2008), 348-354. https://doi.org/10.1016/j.aml.2007.05.005
  6. C. S. Ryoo, T. Kim, R. P. Agarwal, A numerical investigation of the roots of q-polynomials, Inter. J. Comput. Math. 83 (2006), 223-234. https://doi.org/10.1080/00207160600654811
  7. C. S. Ryoo, H. song, R. P. Argawal , On the real roots of the Changhee-Barnes’ q-Bernoulli polynomials, Advan. Stud. Contemp. Math. 9 (2004), 153-163.