Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions
We introduce Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials as generalizations of Bernoulli and Apostol–Euler polynomials, where the role of the derivative is now played by the Dunkl operator on the real line. We use them to find the sum of many different series involving the zeros of Bessel fu...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/182272 |
| Acceso en línea: | https://hdl.handle.net/11441/182272 https://doi.org/10.1016/j.jat.2018.06.001 |
| Access Level: | acceso abierto |
| Palabra clave: | Appell–Dunkl sequences Bernoulli–Dunkl polynomials Apostol–Euler–Dunkl polynomials Dunkl kernel Fourier–Dunkl series Zeros of Bessel functions Rayleigh functions |
| Sumario: | We introduce Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials as generalizations of Bernoulli and Apostol–Euler polynomials, where the role of the derivative is now played by the Dunkl operator on the real line. We use them to find the sum of many different series involving the zeros of Bessel functions. |
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