| Issue |
ITM Web Conf.
Volume 75, 2025
The Second International Conference on Mathematical Analysis and Its Applications (ICONMAA 2024)
|
|
|---|---|---|
| Article Number | 01002 | |
| Number of page(s) | 10 | |
| Section | Real Analysis | |
| DOI | https://doi.org/10.1051/itmconf/20257501002 | |
| Published online | 21 February 2025 | |
On The Convergence of (p1, . . . , pn)-multiple Series
1 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia.
2 Science and Technology Faculty, UIN Maulana Malik Ibrahim Malang, Malang, Indonesia.
3 Center for Mathematics and Society, Faculty of Science, Parahyangan Catholic University, Bandung, Indonesia.
* e-mail: pebrudal@gmail.com
** e-mail: dian.maharani@mat.uin-malang.ac.id
*** e-mail: robby@unpar.ac.id
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.
Key words: p-series / (p1, . . . , pn)-multiple series
© The Authors, published by EDP Sciences, 2025
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