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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Evaluation formulas for Tornheim’s type of alternating double series
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by Hirofumi Tsumura PDF
Math. Comp. 73 (2004), 251-258 Request permission


In this paper, we give some evaluation formulas for Tornheim’s type of alternating series by an elementary and combinatorial calculation of the uniformly convergent series. Indeed, we list several formulas for them by means of Riemann’s zeta values at positive integers.
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Additional Information
  • Hirofumi Tsumura
  • Affiliation: Department of Management Informatics, Tokyo Metropolitan College, Akishima, Tokyo 196-8540 Japan
  • Email:
  • Received by editor(s): April 11, 2002
  • Published electronically: July 14, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Math. Comp. 73 (2004), 251-258
  • MSC (2000): Primary 11M06; Secondary 30B99, 33E20, 40A05, 40B05
  • DOI:
  • MathSciNet review: 2034120