EVALUATION FORMULAS OF CAUCHY-MELLIN TYPE FOR CERTAIN SERIES INVOLVING HYPERBOLIC FUNCTIONS

• KOMORI, YASUSHI

• MATSUMOTO, KOHJI

• TSUMURA, HIROFUMI

抄録

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.

収録刊行物

• Commentarii mathematici Universitatis Sancti Pauli

  Commentarii mathematici Universitatis Sancti Pauli 60 (1-2), 127-142, 2011-12

  Rikkyo Daigaku

詳細情報

• CRID: 1050845763732688640
• NII論文ID: 110008739286
• NII書誌ID: AA00610867
• HANDLE: 2237/20070
• ISSN: 0010258X
• Web Site: https://nagoya.repo.nii.ac.jp/records/17978
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
  • IRDB
  • CiNii Articles