2024-03-29T12:53:00Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00017978
2023-01-16T04:06:15Z
697:698:699
EVALUATION FORMULAS OF CAUCHY-MELLIN TYPE FOR CERTAIN SERIES INVOLVING HYPERBOLIC FUNCTIONS
KOMORI, YASUSHI
52453
MATSUMOTO, KOHJI
52454
TSUMURA, HIROFUMI
52455
We give evaluation formulas for certain Dirichlet series involving hyperbolic factors at some integer points in terms of π and the lemniscate constant, which have the same flavour as the classical formulas due to Cauchy, Mellin and Ramanujan. We then prove analogous formulas for double series involving hyperbolic functions. These formulas are shown via the functional equation for Barnes multiple zeta-functions, proved in a previous paper of the authors.
journal article
Rikkyo Daigaku
2011-12
application/pdf
Commentarii mathematici Universitatis Sancti Pauli
1-2
60
127
142
http://hdl.handle.net/2237/20070
0010-258X
https://nagoya.repo.nii.ac.jp/record/17978/files/8.pdf
eng