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A note on the \((h,q)\)-extension of Bernoulli numbers and Bernoulli polynomials. (English) Zbl 1209.11030

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 \(h,q,n\).

MSC:

11B68 Bernoulli and Euler numbers and polynomials
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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
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