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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| Format: | Article |
| Language: | English |
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EDP Sciences
2025-01-01
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| Series: | ITM Web of Conferences |
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| 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 |
| id | doaj-art-ef60bd2c500e49daa1878927144c3c78 |
| institution | DOAJ |
| issn | 2271-2097 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| 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 |