Inequalities of extended beta and extended hypergeometric functions

We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta functions. The particular cases of those resul...

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Detalles Bibliográficos
Autor principal: Mondal, Saiful R.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5216165/
https://www.ncbi.nlm.nih.gov/pubmed/28111508
http://dx.doi.org/10.1186/s13660-016-1276-9
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author Mondal, Saiful R.
author_facet Mondal, Saiful R.
author_sort Mondal, Saiful R.
collection PubMed
description We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta functions. The particular cases of those results also give the Turán-type inequalities for extended confluent and extended Gaussian hypergeometric functions. Some reverses of Turán-type inequalities are also derived.
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spelling pubmed-52161652017-01-18 Inequalities of extended beta and extended hypergeometric functions Mondal, Saiful R. J Inequal Appl Research We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta functions. The particular cases of those results also give the Turán-type inequalities for extended confluent and extended Gaussian hypergeometric functions. Some reverses of Turán-type inequalities are also derived. Springer International Publishing 2017-01-06 2017 /pmc/articles/PMC5216165/ /pubmed/28111508 http://dx.doi.org/10.1186/s13660-016-1276-9 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Mondal, Saiful R.
Inequalities of extended beta and extended hypergeometric functions
title Inequalities of extended beta and extended hypergeometric functions
title_full Inequalities of extended beta and extended hypergeometric functions
title_fullStr Inequalities of extended beta and extended hypergeometric functions
title_full_unstemmed Inequalities of extended beta and extended hypergeometric functions
title_short Inequalities of extended beta and extended hypergeometric functions
title_sort inequalities of extended beta and extended hypergeometric functions
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5216165/
https://www.ncbi.nlm.nih.gov/pubmed/28111508
http://dx.doi.org/10.1186/s13660-016-1276-9
work_keys_str_mv AT mondalsaifulr inequalitiesofextendedbetaandextendedhypergeometricfunctions

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