Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials
-
1
Universidad de Salamanca
info
-
2
Universidad de Zaragoza
info
-
3
Universidad de La Rioja
info
ISSN: 0025-5718
Argitalpen urtea: 2012
Alea: 81
Zenbakia: 279
Orrialdeak: 1707-1722
Mota: Artikulua
beta Ver similares en nube de resultadosBeste argitalpen batzuk: Mathematics of Computation
Lotura duten proiektuak
Laburpena
We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials Bn(x; λ) in detail. The starting point is their Fourier series on [0, 1] which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze oscillatory phenomena which arise in certain cases. These results are transferred to the Apostol-Euler polynomials En(x; λ) via a simple relation linking them to the Apostol-Bernoulli polynomials. © 2011 American Mathematical Society.