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Mock theta functions and Appell–Lerch sums
Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function [Formula: see text] . The purpose of this paper is to consider the bilateral series for the universal mock theta function [Formula: see text] ....
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer International Publishing
2018
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061538/ https://www.ncbi.nlm.nih.gov/pubmed/30137884 http://dx.doi.org/10.1186/s13660-018-1748-1 |
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author | Chen, Bin |
author_facet | Chen, Bin |
author_sort | Chen, Bin |
collection | PubMed |
description | Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function [Formula: see text] . The purpose of this paper is to consider the bilateral series for the universal mock theta function [Formula: see text] . As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series [Formula: see text] for the third order mock theta function [Formula: see text] is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications. |
format | Online Article Text |
id | pubmed-6061538 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-60615382018-08-09 Mock theta functions and Appell–Lerch sums Chen, Bin J Inequal Appl Research Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function [Formula: see text] . The purpose of this paper is to consider the bilateral series for the universal mock theta function [Formula: see text] . As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series [Formula: see text] for the third order mock theta function [Formula: see text] is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications. Springer International Publishing 2018-07-03 2018 /pmc/articles/PMC6061538/ /pubmed/30137884 http://dx.doi.org/10.1186/s13660-018-1748-1 Text en © The Author(s) 2018 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 Chen, Bin Mock theta functions and Appell–Lerch sums |
title | Mock theta functions and Appell–Lerch sums |
title_full | Mock theta functions and Appell–Lerch sums |
title_fullStr | Mock theta functions and Appell–Lerch sums |
title_full_unstemmed | Mock theta functions and Appell–Lerch sums |
title_short | Mock theta functions and Appell–Lerch sums |
title_sort | mock theta functions and appell–lerch sums |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061538/ https://www.ncbi.nlm.nih.gov/pubmed/30137884 http://dx.doi.org/10.1186/s13660-018-1748-1 |
work_keys_str_mv | AT chenbin mockthetafunctionsandappelllerchsums |