On The Convergence of (p1, . . . , pn)-multiple Series

It is a basic fact that a p-series is a convergent series if p > 1. We generalize the p-series into the form of (p1, . . . , pn)-multiple series. Through a few lemmas, we derive a necessary and sufficient condition for such multiple series to converge. We also obtain the relation between the Riem...

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Main Authors: Zanu Pebrudal, Maharani Dian, Robby
Format: Article
Language:English
Published: EDP Sciences 2025-01-01
Series:ITM Web of Conferences
Subjects:
Online Access:https://www.itm-conferences.org/articles/itmconf/pdf/2025/06/itmconf_iconmaa25_01002.pdf
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author Zanu Pebrudal
Maharani Dian
Robby
author_facet Zanu Pebrudal
Maharani Dian
Robby
author_sort Zanu Pebrudal
collection DOAJ
description It is a basic fact that a p-series is a convergent series if p > 1. We generalize the p-series into the form of (p1, . . . , pn)-multiple series. Through a few lemmas, we derive a necessary and sufficient condition for such multiple series to converge. We also obtain the relation between the Riemann Zeta and Eta functions in double-series form.
format Article
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issn 2271-2097
language English
publishDate 2025-01-01
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series ITM Web of Conferences
spelling doaj-art-ef60bd2c500e49daa1878927144c3c782025-08-20T03:16:28ZengEDP SciencesITM Web of Conferences2271-20972025-01-01750100210.1051/itmconf/20257501002itmconf_iconmaa25_01002On The Convergence of (p1, . . . , pn)-multiple SeriesZanu Pebrudal0Maharani Dian1Robby2Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bandung Institute of TechnologyScience and Technology Faculty, UIN Maulana Malik Ibrahim MalangCenter for Mathematics and Society, Faculty of Science, Parahyangan Catholic UniversityIt is a basic fact that a p-series is a convergent series if p > 1. We generalize the p-series into the form of (p1, . . . , pn)-multiple series. Through a few lemmas, we derive a necessary and sufficient condition for such multiple series to converge. We also obtain the relation between the Riemann Zeta and Eta functions in double-series form.https://www.itm-conferences.org/articles/itmconf/pdf/2025/06/itmconf_iconmaa25_01002.pdfp-series(p1, . . . , pn)-multiple series
spellingShingle Zanu Pebrudal
Maharani Dian
Robby
On The Convergence of (p1, . . . , pn)-multiple Series
ITM Web of Conferences
p-series
(p1, . . . , pn)-multiple series
title On The Convergence of (p1, . . . , pn)-multiple Series
title_full On The Convergence of (p1, . . . , pn)-multiple Series
title_fullStr On The Convergence of (p1, . . . , pn)-multiple Series
title_full_unstemmed On The Convergence of (p1, . . . , pn)-multiple Series
title_short On The Convergence of (p1, . . . , pn)-multiple Series
title_sort on the convergence of p1 pn multiple series
topic p-series
(p1, . . . , pn)-multiple series
url https://www.itm-conferences.org/articles/itmconf/pdf/2025/06/itmconf_iconmaa25_01002.pdf
work_keys_str_mv AT zanupebrudal ontheconvergenceofp1pnmultipleseries
AT maharanidian ontheconvergenceofp1pnmultipleseries
AT robby ontheconvergenceofp1pnmultipleseries