Laguerre-Type Exponentials, Laguerre Derivatives and Applications. A Survey

Laguerrian derivatives and related autofunctions are presented that allow building new special functions determined by the action of a differential isomorphism within the space of analytical functions. Such isomorphism can be iterated every time, so that the resulting construction can be re-submitte...

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Bibliographic Details
Published in:Mathematics (Basel) 2020-11, Vol.8 (11), p.2054
Main Author: Ricci, Paolo
Format: Article
Language:English
Subjects:
Derivatives
Isomorphism
Laguerre-type derivative
Laguerre-type exponentials
Laguerre-type linear dynamical systems
Laguerre-type special functions
Mathematical analysis
Mathematics
multivariable and multi-index Laguerre polynomials
Ordinary differential equations
population dynamics models
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Summary:Laguerrian derivatives and related autofunctions are presented that allow building new special functions determined by the action of a differential isomorphism within the space of analytical functions. Such isomorphism can be iterated every time, so that the resulting construction can be re-submitted endlessly in a cyclic way. Some applications of this theory are made in the field of population dynamics and in the solution of Cauchy’s problems for particular linear dynamical systems.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8112054