Euler Sums and Contour Integral Representations

1998/01/01 by Philippe Flajolet, Bruno Salvy · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebra over a field #Algorithm #Analytic Number Theory Research #Arithmetic zeta function #Backward Euler method #Computation #Euler equations #Euler number (physics) #Euler summation #Euler's formula #Harmonic number #Mathematical analysis #Mathematics #Methods of contour integration #Prime zeta function #Proof of the Euler product formula for the Riemann zeta function #Pure mathematics #Riemann hypothesis #Semi-implicit Euler method #Simple (philosophy)

paper · pdf · doi:10.1080/10586458.1998.10504356

openalex publication_date 1998/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

This paper develops an approach to the evaluation of Euler sums that involve harmonic numbers, either linearly or nonlinearly. We give explicit formulee for several classes of Euler sums in terms of Riemann zeta values. The approach is based on simple contour integral representations and residue computations.

Citations

• On the Evaluation of Euler Sums
• A course of modern analysis an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions
• Explicit evaluation of Euler sums

Cited by

• Evaluation of Triple Euler Sums
• On generalized Lambert function
• Multiple zeta function [wikipedia]