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: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2025-01-01
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| 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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| Summary: | 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. |
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| ISSN: | 2271-2097 |