Article

The Ramanujan Journal

, Volume 16, Issue 1, pp 7-24

A new method in the study of Euler sums

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Abstract

A new method in the study of Euler sums is developed. A host of Euler sums, typically of the form \(\sum_{n=1}^{\infty}\frac{f(n)}{n^{s}}\sum_{m=1}^{n}\frac{g(m)}{m^{t}}\) , are expressed in closed form. Also obtained as a by-product, are some striking recursive identities involving several Dirichlet series including the well-known Riemann Zeta-function.

Keywords

Riemann Zeta function Euler sums Recursions formulas

Mathematics Subject Classification (2000)

40A25 40B05 11M99 33E99