Theory of generalized trigonometric functions: From Laguerre to Airy forms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:468

Article

Dattoli, G.¹  Licciardi, S.¹  Pidatella, R. M.² 

[1] ENEA Frascati Res Ctr, Via Enrico Fermi 45, I-00044 Rome, Italy

[2] Univ Catania, Dept Math & Comp Sci, Viola A Doria 6, I-95125 Catania, Italy

关键词: Trigonometric and hyperbolic functions;    Laguerre polynomials;    Airy forms;    Umbral calculus;    Integral transforms;    Operational methods;   

DOI  :  10.1016/j.jmaa.2018.07.044

来源: Elsevier

【 摘 要 】

We develop a new point of view to introduce families of functions, which can be identified as generalization of the ordinary trigonometric or hyperbolic functions. They are defined using a procedure based on umbral methods, inspired by the Bessel Calculus of Bochner, Cholewinsky and Haimo. We propose further extensions of the method and of the relevant concepts as well and obtain new families of integral transforms allowing the framing of the previous concepts within the context of generalized Borel transform. (C) 2018 Published by Elsevier Inc.

【 授权许可】

Free