Some series involving the Euler zeta function. (English) Zbl 1424.11132
Summary: In this paper, using the Boole summation formula, we obtain a new integral representation of \(n\)-th quasi-periodic Euler functions \(\overline{E}_n(x)\) for \(n=1,2,\ldots\). We also prove several series involving Euler zeta functions \(\zeta_{E}(s)\), which are analogues of the corresponding results by Apostol on some series involving the Riemann zeta function \(\zeta(s)\).
MSC:
| 11M35 | Hurwitz and Lerch zeta functions |
| 33E20 | Other functions defined by series and integrals |
| 33B15 | Gamma, beta and polygamma functions |
| 11B68 | Bernoulli and Euler numbers and polynomials |
Keywords:
Hurwitz-type Euler zeta functions; Euler zeta functions; Euler polynomials; Boole summation formula; quasi-periodic Euler functionsSoftware:
DLMFReferences:
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