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Asymptotic expansions are given for large values of $n$ of the generalizedBernoulli polynomials $B_n^\mu(z)$ and Euler polynomials $E_n^\mu(z)$. In aprevious paper L\'opez and Temme (1999) these polynomials have been consideredfor large values of $\mu$, with $n$ fixed. In the literature no completedescription of the large $n$ asymptotics of the considered polynomials isavailable. We give the general expansions, summarize known results of specialcases and give more details about these results. We use two-point Taylorexpansions for obtaining new type of expansions. The analysis is based oncontour integrals that follow from the generating functions of the polynomials.

Large Degree Asymptotics of Generalized Bernoulli and Euler Polynomials