Abstract
In this paper we observe the structure of the roots ofq-Bernoulli polynomials,β n (w, h|q), using numerical investigation. By numerical experiments, we demonstrate a remarkably regular structure of the real roots ofβ n (w, h|q) forq=−1/5, −1/2. Finally, we give a table for numbers of real and complex zeros ofβ n (w, h|q).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Carlitz,q-Bernoulli numbers and polynomials, Duke Math. J.15 (1948), 987–1000.
T. Kim,Non-Arichimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials, Russ. J. Math. Phys.10 (2003), 91–98.
T. Kim, L. C. Jang, S. H. Rim and H. K. Pak,On the twisted q-Zeta functions and q-Bernoulli polynomials, Far East J. Applied Math.13 (2003), 13–21.
T. Kim, S. H. Rim,Generalized Carlitz's q-Bernoulli Numbers in the p-adic number field, Adv. Stud. Contemp. Math.2 (2000), 9–19.
Author information
Authors and Affiliations
Corresponding author
Additional information
Cheon Seoung Ryoo received his Ph. D. degree from Kyushu University in 1998. His research interests focus on the numerical verification method and scientific computing.
Rights and permissions
About this article
Cite this article
Ryoo, C.S. Structure of the zeros ofq-Bernoulli polynomials. JAMC 17, 49–58 (2005). https://doi.org/10.1007/BF02936040
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02936040