Explicit formulas of some mixed Euler sums via alternating multiple zeta values. (English) Zbl 1443.11184
Summary: In this paper, we present some new identities for (alternating) multiple zeta values and (alternating) Euler sums by using the method of iterated-integral representations of series. In particular, we prove five new evaluations of (alternating) mixed Euler sums via (alternating) multiple zeta values. Some interesting consequences and illustrative examples are considered.
MSC:
| 11M32 | Multiple Dirichlet series and zeta functions and multizeta values |
| 11M06 | \(\zeta (s)\) and \(L(s, \chi)\) |
| 40B05 | Multiple sequences and series |
| 33E20 | Other functions defined by series and integrals |
Keywords:
multiple zeta (star) values; alternating multiple zeta (star) values; multiple harmonic (star) sums; alternating multiple harmonic (star) sums; Euler sumsReferences:
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