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.
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Basu, A. A new method in the study of Euler sums. Ramanujan J 16, 7–24 (2008). https://doi.org/10.1007/s11139-007-9089-6
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DOI: https://doi.org/10.1007/s11139-007-9089-6