Radar/Sonar detection and Laguerre functions

Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics ◽

10.3390/math9090984 ◽

2021 ◽

Vol 9 (9) ◽

pp. 984

Author(s):

Pedro J. Miana ◽

Natalia Romero

Keyword(s):

Integral Representation ◽

Special Functions ◽

Laguerre Polynomials ◽

Function Spaces ◽

Laguerre Functions ◽

Addition Formula ◽

Lebesgue Spaces ◽

Rodrigues Formula ◽

Generalized Laguerre Polynomials ◽

New Family

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

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Spectral method for Multi-dimensional problems of high order on unbounded domains using generalized Laguerre functions

International Journal of Computer Mathematics ◽

10.1080/00207160.2021.1872784 ◽

2021 ◽

pp. 1-19

Author(s):

Chao Zhang ◽

Dongya Tao ◽

Pan Ding

Keyword(s):

Spectral Method ◽

Unbounded Domains ◽

High Order ◽

Laguerre Functions

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Voigt Transform and Umbral Image

Mathematical and Computational Applications ◽

10.3390/mca25030049 ◽

2020 ◽

Vol 25 (3) ◽

pp. 49

Author(s):

Silvia Licciardi ◽

Rosa Maria Pidatella ◽

Marcello Artioli ◽

Giuseppe Dattoli

Keyword(s):

Spectroscopic Studies ◽

Higher Order ◽

Point Of View ◽

The Other ◽

Pivotal Role ◽

Umbral Calculus ◽

Laguerre Functions ◽

Hermite And Laguerre Functions ◽

Higher Order Functions ◽

Voigt Function

In this paper, we show that the use of methods of an operational nature, such as umbral calculus, allows achieving a double target: on one side, the study of the Voigt function, which plays a pivotal role in spectroscopic studies and in other applications, according to a new point of view, and on the other, the introduction of a Voigt transform and its possible use. Furthermore, by the same method, we point out that the Hermite and Laguerre functions, extension of the corresponding polynomials to negative and/or real indices, can be expressed through a definition in a straightforward and unified fashion. It is illustrated how the techniques that we are going to suggest provide an easy derivation of the relevant properties along with generalizations to higher order functions.

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