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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Some identities involving harmonic numbers


Author: Jürgen Spiess
Journal: Math. Comp. 55 (1990), 839-863
MSC: Primary 05A19; Secondary 11B37, 68R05
MathSciNet review: 1023769
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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

DOI: http://dx.doi.org/10.1090/S0025-5718-1990-1023769-6
PII: S 0025-5718(1990)1023769-6
Keywords: Harmonic numbers, symbolic computation, computational analysis, combinatorial identities
Article copyright: © Copyright 1990 American Mathematical Society