<i>q</i>-Functions and Distributions, Operational and Umbral Methods

The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials. These methods have helped to frame either elementary and special functions within the same logical context. Methods of Umbral and operational cal...

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Autores principales:	Giuseppe Dattoli, Silvia Licciardi, Bruna Germano, Maria Renata Martinelli
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	operators theory 44A99, 47B99, 47A62 umbral methods 05A40 special functions 33C52, 33C65, 33C99, 33B10, 33B15 Hermite polynomials 33C45 calculus Tsallis 60E99 Student’s distribution 60E05 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/74184f40fd6e4102a877f52f9fe7d501
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spelling	oai:doaj.org-article:74184f40fd6e4102a877f52f9fe7d5012021-11-11T18:14:13Z<i>q</i>-Functions and Distributions, Operational and Umbral Methods10.3390/math92126642227-7390https://doaj.org/article/74184f40fd6e4102a877f52f9fe7d5012021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2664https://doaj.org/toc/2227-7390The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials. These methods have helped to frame either elementary and special functions within the same logical context. Methods of Umbral and operational calculus have been embedded in a powerful and efficient analytical tool, which will be applied to the study of the properties of distributions such as Tsallis, Weibull and Student’s. We state that they can be viewed as standard Gaussian distributions and we take advantage of the relevant properties to infer those of the aforementioned distributions.Giuseppe DattoliSilvia LicciardiBruna GermanoMaria Renata MartinelliMDPI AGarticleoperators theory 44A99, 47B99, 47A62umbral methods 05A40special functions 33C52, 33C65, 33C99, 33B10, 33B15Hermite polynomials 33C45calculus Tsallis 60E99Student’s distribution 60E05MathematicsQA1-939ENMathematics, Vol 9, Iss 2664, p 2664 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	operators theory 44A99, 47B99, 47A62 umbral methods 05A40 special functions 33C52, 33C65, 33C99, 33B10, 33B15 Hermite polynomials 33C45 calculus Tsallis 60E99 Student’s distribution 60E05 Mathematics QA1-939
spellingShingle	operators theory 44A99, 47B99, 47A62 umbral methods 05A40 special functions 33C52, 33C65, 33C99, 33B10, 33B15 Hermite polynomials 33C45 calculus Tsallis 60E99 Student’s distribution 60E05 Mathematics QA1-939 Giuseppe Dattoli Silvia Licciardi Bruna Germano Maria Renata Martinelli <i>q</i>-Functions and Distributions, Operational and Umbral Methods
description	The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials. These methods have helped to frame either elementary and special functions within the same logical context. Methods of Umbral and operational calculus have been embedded in a powerful and efficient analytical tool, which will be applied to the study of the properties of distributions such as Tsallis, Weibull and Student’s. We state that they can be viewed as standard Gaussian distributions and we take advantage of the relevant properties to infer those of the aforementioned distributions.
format	article
author	Giuseppe Dattoli Silvia Licciardi Bruna Germano Maria Renata Martinelli
author_facet	Giuseppe Dattoli Silvia Licciardi Bruna Germano Maria Renata Martinelli
author_sort	Giuseppe Dattoli
title	<i>q</i>-Functions and Distributions, Operational and Umbral Methods
title_short	<i>q</i>-Functions and Distributions, Operational and Umbral Methods
title_full	<i>q</i>-Functions and Distributions, Operational and Umbral Methods
title_fullStr	<i>q</i>-Functions and Distributions, Operational and Umbral Methods
title_full_unstemmed	<i>q</i>-Functions and Distributions, Operational and Umbral Methods
title_sort	<i>q</i>-functions and distributions, operational and umbral methods
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/74184f40fd6e4102a877f52f9fe7d501
work_keys_str_mv	AT giuseppedattoli iqifunctionsanddistributionsoperationalandumbralmethods AT silvialicciardi iqifunctionsanddistributionsoperationalandumbralmethods AT brunagermano iqifunctionsanddistributionsoperationalandumbralmethods AT mariarenatamartinelli iqifunctionsanddistributionsoperationalandumbralmethods
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<i>q</i>-Functions and Distributions, Operational and Umbral Methods

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