Abstract
We present a unified approach which gives completely elementary proofs of three weighted sum formulae for double zeta values. This approach also leads to new evaluations of sums involving the harmonic numbers, the alternating double zeta values, and the Mordell–Tornheim double sum. We discuss a heuristic for finding or dismissing the existence of similar simple sums. We also produce some new sums from recursions involving the Riemann zeta and the Dirichlet beta functions.
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Acknowledgements
The author wishes to thank John Zucker and Wadim Zudilin for illuminating discussions.
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Wan, J. (2013). Some Notes on Weighted Sum Formulae for Double Zeta Values. In: Borwein, J., Shparlinski, I., Zudilin, W. (eds) Number Theory and Related Fields. Springer Proceedings in Mathematics & Statistics, vol 43. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6642-0_19
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DOI: https://doi.org/10.1007/978-1-4614-6642-0_19
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