In this paper we consider a new type of the q-Apostol Bernoulli numbers and polynomials. Firstly, we define the q-Apostol Bernoulli numbers and polynomials by making use of their generating function. Also, we observe many properties, i.e., the recurrence formula, the difference equation, the differential relation.
Keywords:The second kind q-Apostol Bernoulli polynomials, the second kind q-Apostol Bernoulli numbers, zeta function.
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