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Zbl 1155.40002
Basu, Ankur
A new method in the study of Euler sums. (English)
[J] Ramanujan J. 16, No. 1, 7-24 (2008). ISSN 1382-4090; ISSN 1572-9303/e

Summary: 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.

MSC 2000:: *40A25 Approximation to limiting values
40B05 Multiple sequences and series
11M99 Analytic theory of zeta and L-functions
33E99 Special functions

Keywords: Riemann zeta function; Euler sums; recursions formulas

Cited in: Zbl 1234.11022 Zbl 1198.05010

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