Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc68f6b750603269e81289 |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc68f6b750603269e81289 |
| Access Level: | acceso abierto |
| Palabra clave: | Apostol-Bernoulli polynomials Apostol-Euler polynomials Asymptotic estimates Fourier series |
| Sumario: | 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. |
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