Chunli Li, Wenchang Chu, “Integral Representations of $\mathrm{\zeta}(m)$”, Матем. заметки, 2024, том 115, выпуск 4,страницы 569

Статьи, опубликованные в английской версии журнала

Integral Representations of $\mathrm{\zeta}(m)$

Chunli Li^a, Wenchang Chu^b

^a School of Mathematics and Statistics, Zhoukou Normal University, P. R. China
^b Lecce University, Italy

Аннотация: An open problem about integral representation of $\zeta(2n)$, proposed recently by Pain (2023), is resolved by integration by parts. More general integrals are examined by manipulating the beta integral and digamma function.

Ключевые слова: Riemann zeta function, generating function, beta integral, digamma function.

Поступило: 28.11.2023
Исправленный вариант: 13.01.2024

Язык публикации: английский