Large degree asymptotics of generalized Bernoulli and Euler polynomials
Copyright policy )Large degree asymptotics of generalized Bernoulli and Euler polynomials
Asymptotic expansions are given for large values of $n$ of the generalized Bernoulli polynomials $B_n^μ(z)$ and Euler polynomials $E_n^μ(z)$. In a previous paper López and Temme (1999) these polynomials have been considered for large values of $μ$, 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.
20 pages, 1 figure
- Dutch Research Council Netherlands
- Centrum Wiskunde & Informatica Netherlands
- STICHTING CENTRUM VOOR WISKUNDE EN INFORMATICA Netherlands
- Universidad Publica De Navarra Spain
Asymptotic approximations, asymptotic expansions (steepest descent, etc.), generalized Bernoulli polynomials, Applied Mathematics, 11B68, 30E10, 41A60., asymptotic expansions, Asymptotic expansions, Generalized Bernoulli polynomials, generating function, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Generalized Euler polynomials, Bernoulli and Euler numbers and polynomials, generalized Euler polynomials, Cauchy integral representation, Analysis
Asymptotic approximations, asymptotic expansions (steepest descent, etc.), generalized Bernoulli polynomials, Applied Mathematics, 11B68, 30E10, 41A60., asymptotic expansions, Asymptotic expansions, Generalized Bernoulli polynomials, generating function, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Generalized Euler polynomials, Bernoulli and Euler numbers and polynomials, generalized Euler polynomials, Cauchy integral representation, Analysis
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