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

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