Log-convexity and the overpartition function

Let [Formula: see text] denote the overpartition function. In this paper, we obtain an inequality for the sequence [Formula: see text] which states that [Formula: see text] where [Formula: see text] is a non-negative real number, [Formula: see text] is a positive integer depending on [Formula: see t...

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Autor principal: Mukherjee, Gargi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9883361/
https://www.ncbi.nlm.nih.gov/pubmed/36721669
http://dx.doi.org/10.1007/s11139-022-00578-0
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author Mukherjee, Gargi
author_facet Mukherjee, Gargi
author_sort Mukherjee, Gargi
collection PubMed
description Let [Formula: see text] denote the overpartition function. In this paper, we obtain an inequality for the sequence [Formula: see text] which states that [Formula: see text] where [Formula: see text] is a non-negative real number, [Formula: see text] is a positive integer depending on [Formula: see text] , and [Formula: see text] is the difference operator with respect to n. This inequality consequently implies [Formula: see text] -convexity of [Formula: see text] and [Formula: see text] . Moreover, it also establishes the asymptotic growth of [Formula: see text] by showing [Formula: see text]
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spelling pubmed-98833612023-01-29 Log-convexity and the overpartition function Mukherjee, Gargi Ramanujan J Article Let [Formula: see text] denote the overpartition function. In this paper, we obtain an inequality for the sequence [Formula: see text] which states that [Formula: see text] where [Formula: see text] is a non-negative real number, [Formula: see text] is a positive integer depending on [Formula: see text] , and [Formula: see text] is the difference operator with respect to n. This inequality consequently implies [Formula: see text] -convexity of [Formula: see text] and [Formula: see text] . Moreover, it also establishes the asymptotic growth of [Formula: see text] by showing [Formula: see text] Springer US 2022-05-13 2023 /pmc/articles/PMC9883361/ /pubmed/36721669 http://dx.doi.org/10.1007/s11139-022-00578-0 Text en © The Author(s) 2022, corrected publication 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Mukherjee, Gargi
Log-convexity and the overpartition function
title Log-convexity and the overpartition function
title_full Log-convexity and the overpartition function
title_fullStr Log-convexity and the overpartition function
title_full_unstemmed Log-convexity and the overpartition function
title_short Log-convexity and the overpartition function
title_sort log-convexity and the overpartition function
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9883361/
https://www.ncbi.nlm.nih.gov/pubmed/36721669
http://dx.doi.org/10.1007/s11139-022-00578-0
work_keys_str_mv AT mukherjeegargi logconvexityandtheoverpartitionfunction

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