Guide to the Umbral Calculus, a Different Mathematical Language by Silvia Licciardi

Author:Silvia Licciardi
Language: eng
Format: epub
Publisher: World Scientific Publishing Company
Published: 2022-01-15T00:00:00+00:00

5.2.1 Generalized Trigonometric Functions, Ordinary and Higher-order Bessel Functions

The Bessel functions are characterized by a continuous variable and by a real or complex index. A fairly natural extension of the function defined by Eq. (5.2.9) is therefore provided by the l–t functions, associated with the α-order Bessel-like function (7.5.12), for m = 1, then

Corollary 31. We get the function

which is an eigenfunction of the operator [70]

We can now proceed as in the previous section, by noting that the polynomials

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