EULER–ZAGIER SUMS VIA TRIGONOMETRIC SERIES
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Dosyalar
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Publishing House of the Romanian Academy
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this note, we study the evaluations of Euler sums via trigonometric series. It is a commonly believed conjecture that for an even weight greater than seven, Euler sums cannot be evaluated in terms of the special values of the Riemann zeta function. For an even weight, we reduce the evaluations of Euler sums into the evaluations of double series and integrals of products of Clausen functions. We also re-evaluate Euler sums of odd weight using a new method based on trigonometric series. © 2023 Editura Academiei Romane. All rights reserved.
Açıklama
Anahtar Kelimeler
Euler sums, trigonometric series
Kaynak
WoS Q Değeri
Q4
