Some Notes on Weighted Sum Formulae for Double Zeta Values

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.KeywordsClosed FormZeta FunctionPartial FractionRiemann Zeta FunctionHarmonic NumberThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.