A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions. We emphasize the role of the spherical Bessel functions and a family of associated auxiliary polynomials, as transition elements between these families of functions. The consequences of this point of view and the relevant impact on the study of the properties of special functions is carefully discussed
Giuseppe Dattoli, Silvia Licciardi, Emanuele Di Palma, Elio Sabia (2017). From circular to Bessel functions: a transition through the umbral method. FRACTAL AND FRACTIONAL, 1(1) [10.3390/fractalfract1010009].
From circular to Bessel functions: a transition through the umbral method
Silvia Licciardi
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2017-11-08
Abstract
A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions. We emphasize the role of the spherical Bessel functions and a family of associated auxiliary polynomials, as transition elements between these families of functions. The consequences of this point of view and the relevant impact on the study of the properties of special functions is carefully discussed
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