Academic Journal
A note on some alternating series involving zeta and multiple zeta values
| العنوان: | A note on some alternating series involving zeta and multiple zeta values |
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| المؤلفون: | Coppo, Marc-Antoine |
| المساهمون: | Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA) |
| المصدر: | ISSN: 0022-247X. |
| بيانات النشر: | HAL CCSD Elsevier |
| سنة النشر: | 2019 |
| المجموعة: | HAL Université Côte d'Azur |
| مصطلحات موضوعية: | Ramanujan summation of divergent series, multiple zeta values, Gregory coefficients of higher order, Bernoulli numbers, Stirling numbers of the first kind, harmonic zeta function, Riemann zeta function, harmonic numbers, Bernoulli numbers of the second kind, Stirling numbers of the second kind, MSC (2010) : 11B73, 11B75, 11M06, 11M32, 40G99, 41A58, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] |
| الوصف: | International audience ; In this article, we study a class of conditionally convergent alternating series including, as a special case, the famous series $\sum_{n\geq 2}(−1)^n \frac{ζ(n}{n}$ which links Euler’s constant $\gamma$ to special values of the Riemann zeta function at positive integers. We give several new relations of the same kind. Among other things, we show the existence of a similar relation for the Apostol-Vu harmonic zeta function which have never been noticed before. We also highlight a deep connection with the Ramanujan summation of certain divergent series which originally motivated this work. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | hal-01735381; https://hal.univ-cotedazur.fr/hal-01735381; https://hal.univ-cotedazur.fr/hal-01735381v8/document; https://hal.univ-cotedazur.fr/hal-01735381v8/file/JMAA3mod.pdf |
| DOI: | 10.1016/j.jmaa.2019.03.057 |
| الاتاحة: | https://hal.univ-cotedazur.fr/hal-01735381 https://hal.univ-cotedazur.fr/hal-01735381v8/document https://hal.univ-cotedazur.fr/hal-01735381v8/file/JMAA3mod.pdf https://doi.org/10.1016/j.jmaa.2019.03.057 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.64A3F828 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.jmaa.2019.03.057 |
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