Large degree asymptotics of generalized Bernoulli and Euler polynomials
Journal of Mathematical Analysis and Applications , Volume 363 - Issue 1 p. 197- 208
Asymptotic expansions are given for large values of $n$ of the generalized Bernoulli polynomials $B_n^\mu(z)$ and Euler polynomials $E_n^\mu(z)$. In a previous paper L\'opez and Temme (1999) these polynomials have been considered for large values of $\mu$, with $n$ fixed. In the literature no complete description of the large $n$ asymptotics of the considered polynomials is available. We give the general expansions, summarize known results of special cases and give more details about these results. We use two-point Taylor expansions for obtaining new type of expansions. The analysis is based on contour integrals that follow from the generating functions of the polynomials.
|asymptotic expansions, generalized Bernoulli polynomials, generalized Euler polynomials|
|Bernoulli and Euler numbers and polynomials (msc 11B68)|
|Journal of Mathematical Analysis and Applications|
López, J.L, & Temme, N.M. (2010). Large degree asymptotics of generalized Bernoulli and Euler polynomials. Journal of Mathematical Analysis and Applications, 363(1), 197–208.