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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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/2054 |
| _version_ | 1827702059097391104 |
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| author | Paolo Emilio Ricci |
| author_facet | Paolo Emilio Ricci |
| author_sort | Paolo Emilio Ricci |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T14:46:58Z |
| format | Article |
| id | doaj.art-9ae27614f7694736bea0465ffe25217e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:46:58Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9ae27614f7694736bea0465ffe25217e2023-11-20T21:20:29ZengMDPI AGMathematics2227-73902020-11-01811205410.3390/math8112054Laguerre-Type Exponentials, Laguerre Derivatives and Applications. A SurveyPaolo Emilio Ricci0Department of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, ItalyLaguerrian 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.https://www.mdpi.com/2227-7390/8/11/2054Laguerre-type derivativeLaguerre-type exponentialsLaguerre-type special functionsmultivariable and multi-index Laguerre polynomialspopulation dynamics modelsLaguerre-type linear dynamical systems |
| spellingShingle | Paolo Emilio Ricci Laguerre-Type Exponentials, Laguerre Derivatives and Applications. A Survey Mathematics Laguerre-type derivative Laguerre-type exponentials Laguerre-type special functions multivariable and multi-index Laguerre polynomials population dynamics models Laguerre-type linear dynamical systems |
| title | Laguerre-Type Exponentials, Laguerre Derivatives and Applications. A Survey |
| title_full | Laguerre-Type Exponentials, Laguerre Derivatives and Applications. A Survey |
| title_fullStr | Laguerre-Type Exponentials, Laguerre Derivatives and Applications. A Survey |
| title_full_unstemmed | Laguerre-Type Exponentials, Laguerre Derivatives and Applications. A Survey |
| title_short | Laguerre-Type Exponentials, Laguerre Derivatives and Applications. A Survey |
| title_sort | laguerre type exponentials laguerre derivatives and applications a survey |
| topic | Laguerre-type derivative Laguerre-type exponentials Laguerre-type special functions multivariable and multi-index Laguerre polynomials population dynamics models Laguerre-type linear dynamical systems |
| url | https://www.mdpi.com/2227-7390/8/11/2054 |
| work_keys_str_mv | AT paoloemilioricci laguerretypeexponentialslaguerrederivativesandapplicationsasurvey |