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Calculating zeros of the twisted q-Genocchi polynomials

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In this paper we construct the twisted q-Genocchi numbers Gn,q,w and polynomials Gn,q,w(x). We also observe the behavior of complex roots of the the twisted q-Genocchi polynomials Gn,q,w(x), using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the twisted q-Genocchi polynomials Gn,q,w(x). Finally, we give a table for the solutions of the twisted q-Genocchi polynomials..

Abstract

In this paper we construct the twisted q-Genocchi numbers Gn,q,w and polynomials Gn,q,w(x). We also observe the behavior of complex roots of the the twisted q-Genocchi polynomials Gn,q,w(x), using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the twisted q-Genocchi polynomials Gn,q,w(x). Finally, we give a table for the solutions of the twisted q-Genocchi polynomials..

참고문헌 (11)

  1. Cenkci, M, "q-adic interpolation functions and kummer type congruence for q-twisted and q-generalized twisted Euler numbers", Advan. Stud. Contemp. Math., 9, pp.203~216 (2004)
  2. Kreweras, G, "An Additive Generation for the Genocchi Numbers and Two of its Enumerative Meanings", Bull. Inst. Combin. Appl., 20, pp.99~103 (1997)
  3. T. Kim, "Note on q-Genocchi numbers and polynomials", Advanced Studies in Contemporary Mathematics, 17(1), pp.9~15 (2008), 장전수학회
  4. Kim, T., "On the q-extension of Euler and Genocchi numbers", J. Math. Anal. Appl., 326, pp.1458~1465 (2007)
  5. Kim, T, "A note on q-Euler and Genocchi numbers", Proc. Japan Acad., 77, pp.139~141 (2001)
  6. Kim, T, "Exploring the q-Riemann Zeta function and q-Bernoulli polynomials", Discrete Dynamics in Nature and Society, 2005(2), pp.171~181 (2005)
  7. Ryoo, C.S, "A numerical computation on the structure of the roots of (h, q)-extension of Genocchi polynomials", Mathematical and Computer Modelling, 49, pp.463~474 (2009)
  8. C. S. Ryoo, "Calculating zeros of the twisted Genocchi polynomials", Advanced Studies in Contemporary Mathematics, 17(2), pp.147~159 (2008), 장전수학회
  9. Ryoo, C.S, "Exploring the multiple Changhee q-Bernoulli polynomials", Inter. J. Comput. Math., 82(4), pp.483~493 (2005)
  10. Ryoo,C.S, "On the roots of the q-analogue of Euler-Barnes’ polynomials", Advan. Stud. Contemp. Math., 9, pp.153~163 (2004)
  11. 유천성, "On the real roots of the q-Hurwitz zeta-function", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 11(2), pp.205~214 (2008), 장전수학회

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