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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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Some identities involving harmonic numbers
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by Jürgen Spiess PDF
Math. Comp. 55 (1990), 839-863 Request permission

Abstract:

Let ${H_n}$ denote the nth harmonic number. Explicit formulas for sums of the form $\sum {a_k}{H_k}$ or $\sum {a_k}{H_k}{H_{n - k}}$ are derived, where the ${a_k}$ are simple functions of k. These identities are generalized in a natural way by means of generating functions.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 55 (1990), 839-863
  • MSC: Primary 05A19; Secondary 11B37, 68R05
  • DOI: https://doi.org/10.1090/S0025-5718-1990-1023769-6
  • MathSciNet review: 1023769