Elementary methods for evaluating Jordan's sums and analogous Euler's type sums and for setting a sigma sum theorem

2013/01/31 by Guy Bastien, Bastien, Guy
Mathematics · #11M32 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M32

paper · pdf · doi:10.48550/arxiv.1301.7662

29 pages

arxiv created 2013/01/31 · openalex publication_date 2013/01/31 · arxiv updated 2013/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a complete and elementary proofs of "Jordan's sums" and study Euler's types sums. In particular we give a formula for the sum of series with same weight, which is similar to this one of classical 2-Euler's sums.

Related

• Elementary evaluations of some Euler sums
• New Results for Euler Sums
• Explicit Evaluations for Several Variants of Euler Sums
• Determination of some generalised Euler sums involving the digamma function
• Alternating Euler T-sums and Euler S-sums