Abstract
The main objective of this paper is to introduce and investigate two new classes of generalized Apostol-Bernoulli polynomials B<SUB>n</SUB><SUP>[</SUP><SUP>m-1,</SUP>α<SUP>]</SUP>(x;c,α;λ) and Apostol-Euler polynomials ε<SUB>n</SUB><SUP>[m-1,</SUP>α<SUP>]</SUP>(x;c,α;λ). In particular, we obtain addition formula for the new class of the generalized Apostol-Bernoulli polynomials. We also give some recurrence relations and Raabe relations for these polynomials.
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