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Zbl 0971.40001
Basu, Ankur; Apostol, Tom M.
A new method for investigating Euler sums. (English)
[J] Ramanujan J. 4, No.4, 397-419 (2000). ISSN 1382-4090; ISSN 1572-9303/e

Summary: Euler discovered a recursion formula for the Riemann zeta function evaluated at the even integers. He also evaluated special Dirichlet series whose coefficients are the partial sums of the harmonic series. This paper introduces a new method for deducing Euler's formulas as well as a host of new relations, not only for the zeta function but for several allied functions.

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

Keywords: Euler sums; recursion formulas; harmonic series; Riemann zeta function

Cited in: Zbl 1234.11022

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