Recurrence relations for Apostol-Bernoulli , -Euler and -Genocchi polynomials of higher order

Abstract: In \cite{luo2006,luosri2005}, Luo and Srivastava introduced some generalizations of the Apostol -Bernoulli polynomials and the Apostol-Euler polynomials. The main object of this paper is to extend the result of \cite{prevost2010} to these generalized polynomials. More precisely, using the Pad\'{e} approximation of the exponential function, we obtain recurrence relations for Apostol-Bernoulli, Euler and also Genocchi polynomials of higher order. As an application we prove lacunary relation for some particular cases.