Experimental Mathematics

Euler sums and contour integral representations

Philippe Flajolet and Bruno Salvy

Abstract

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

Article information

Source
Experiment. Math., Volume 7, Issue 1 (1998), 15-35.

Dates
First available in Project Euclid: 14 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1047674270

Mathematical Reviews number (MathSciNet)
MR1618286

Zentralblatt MATH identifier
0920.11061

Subjects
Primary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
Secondary: 11Y60: Evaluation of constants

Citation

Flajolet, Philippe; Salvy, Bruno. Euler sums and contour integral representations. Experiment. Math. 7 (1998), no. 1, 15--35. https://projecteuclid.org/euclid.em/1047674270


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