A note on q-Bernoulli numbers and polynomials

Abstract Recently, B. A. Kupershmidt have constructed a reflection symmetries of q-Bernoulli polynomials (see [9]). In this paper we give another construction of a q-Bernoulli polynomials, which form Barnes’ multiple Bernoulli polynomials at q=1, cf. [1, 13, 14]. By using q-Volkenborn integration, we can also investigate the properties of the reflection symmetries of these’ q-Bernoulli polynomials.

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