The Riemann zeta function and classes of infinite series | Zendy

Horst Alzer | Zendy; Junesang Choi | Zendy

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The Riemann zeta function and classes of infinite series

Author(s) -

Horst Alzer,

Junesang Choi

Publication year - 2017

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm1702386a

Subject(s) - mathematics , riemann zeta function , proof of the euler product formula for the riemann zeta function , series (stratigraphy) , euler's formula , riemann hypothesis , particular values of riemann zeta function , constant (computer programming) , harmonic number , pure mathematics , riemann xi function , arithmetic zeta function , function (biology) , prime zeta function , mathematical analysis , paleontology , evolutionary biology , computer science , biology , programming language

We present one-parameter series representations for the following series involving the Riemann zeta function Σ∞n=3 n odd ζ(n)/n sn and Σ∞n=2 n even ζ(n) n sn and we apply our results to obtain new representations for some mathematical constants such as the Euler (or Euler-Mascheroni) constant, the Catalan constant, log 2, ζ(3) and π.

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