Ryoo, C. S.; Kim, T. A note on the \((h,q)\)-extension of Bernoulli numbers and Bernoulli polynomials. (English) Zbl 1209.11030 Discrete Dyn. Nat. Soc. 2010, Article ID 807176, 11 p. (2010). The \((h,q)\)-extended Bernoulli polynomials are defined by the generating series \[ \frac{h\log q+t}{q^he^t-1}e^{xt}=\sum_{n=0}^\infty B_{n,q}^{(h)}(x)\frac{t^n}{n!}. \] The authors present tables and figures with the zeros of the polynomials \(B_{n,q}^{(h)}(x)\) for several values of \(h,q,n\). Reviewer: Florin Nicolae (Berlin) Cited in 1 Document MSC: 11B68 Bernoulli and Euler numbers and polynomials Keywords:Bernoulli polynomials PDFBibTeX XMLCite \textit{C. S. Ryoo} and \textit{T. Kim}, Discrete Dyn. Nat. Soc. 2010, Article ID 807176, 11 p. (2010; Zbl 1209.11030) Full Text: DOI EuDML References: [1] T. Kim, “Note on the Euler q-zeta functions,” Journal of Number Theory, vol. 129, no. 7, pp. 1798-1804, 2009. · Zbl 1221.11231 · doi:10.1016/j.jnt.2008.10.007 [2] T. Kim, “q-Euler numbers and polynomials associated with p-adic q-integrals,” Journal of Nonlinear Mathematical Physics, vol. 14, no. 1, pp. 15-27, 2007. · Zbl 1159.11049 · doi:10.1016/j.camwa.2006.12.028 [3] T. Kim, “On p-adic interpolating function for q-Euler numbers and its derivatives,” Journal of Mathematical Analysis and Applications, vol. 339, no. 1, pp. 598-608, 2008. · Zbl 1160.11013 · doi:10.1016/j.jmaa.2007.07.027 [4] T. Kim, “q-Volkenborn integration,” Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288-299, 2002. · Zbl 1092.11045 [5] T. Kim and Seog-Hoon Rim, “Generalized Carlitz’s q-Bernoulli numbers in the p-adic number field,” Advanced Studies in Contemporary Mathematics, vol. 2, pp. 9-19, 2000. · Zbl 1050.11020 [6] C. S. Ryoo and T. Kim, “An analogue of the zeta function and its applications,” Applied Mathematics Letters, vol. 19, no. 10, pp. 1068-1072, 2006. · Zbl 1112.11013 · doi:10.1016/j.aml.2005.11.019 [7] C. S. Ryoo, “A numerical computation on the structure of the roots of q-extension of Genocchi polynomials,” Applied Mathematics Letters, vol. 21, no. 4, pp. 348-354, 2008. · Zbl 1133.33309 · doi:10.1016/j.aml.2007.05.005 [8] C. S. Ryoo, “Calculating zeros of the twisted Genocchi polynomials,” Advanced Studies in Contemporary Mathematics, vol. 17, no. 2, pp. 147-159, 2008. · Zbl 1171.11012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.