Structure of the zeros ofq-Bernoulli polynomials



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).

AMS Mathematics Subject Classification

81T99 26A33 58B99 

Key words and phrases

Numerical experiments Bernoulli polynomials q-Bernoulli polynomials 


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  1. 1.
    L. Carlitz,q-Bernoulli numbers and polynomials, Duke Math. J.15 (1948), 987–1000.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    T. Kim,Non-Arichimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials, Russ. J. Math. Phys.10 (2003), 91–98.MATHMathSciNetGoogle Scholar
  3. 3.
    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.MATHMathSciNetGoogle Scholar
  4. 4.
    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.MATHMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2005

Authors and Affiliations

  1. 1.Department of MathematicsHannam UniversityDaejeonKorea

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