2024-08-06T10:11:59Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00018325
2023-01-16T04:42:38Z
697:698:699
Barnes multiple zeta-functions, Ramanujan’s formula, and relevant series involving hyperbolic functions
Komori, Yasushi
53350
Matsumoto, Kohji
53351
Tsumura, Hirofumi
53352
In the former part of this paper, we give functional equations for Barnes multiple zeta-functions and consider some relevant results. In particular, we show that Ramanujan’s classical formula for the Riemann zeta values can be derived from functional equations for Barnes zetafunctions. In the latter half part, we generalize some evaluation formulas for certain series involving hyperbolic functions in terms of Bernoulli polynomials. The original formulas were classically given by Cauchy, Mellin, Ramanujan, and later recovered and reformulated by Berndt. From our consideration, we give multiple versions of these known formulas.
journal article
Ramanujan Mathematical Society
2013-03
application/pdf
Journal of the Ramanujan Mathematical Society
1
28
49–69
49–69
http://hdl.handle.net/2237/20427
0970-1249
https://nagoya.repo.nii.ac.jp/record/18325/files/2.pdf
eng