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In the present paper, we obtain new interesting relations and identities ofthe Apostol-Bernoulli polynomials of higher order, which are derived using aBernoulli polynomial basis. Finally, by utilizing our method, we also deriveformulas for the convolutions of Bernoulli and Euler polynomials, expressed viaApostol-Bernoulli polynomials of higher order.

Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis