Some notes on weighted sum formulae for double zeta values

Title: Some notes on weighted sum formulae for double zeta values
Creator: Wan, James
Relation: Number Theory and Related Fields: In Memory of Alf van der Poorten p. 361-379
Relation: Springer Proceedings in Mathematics & Statistics 43
Publisher Link: http://dx.doi.org/10.1007/978-1-4614-6642-0_19
Publisher: Springer New York
Resource Type: book chapter
Date: 2013
Description: 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.
Subject: double zeta values; Riemann zeta; Dirichlet beta; weighted sum formulae
Identifier: http://hdl.handle.net/1959.13/1068193
Identifier: uon:18575
Identifier: ISBN:9781461466413
Language: eng