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Series Involving the Zeta Functions and a Family of Generalized Goldbach–Euler Series

Junesang Choi and Hari M. Srivastava
The American Mathematical Monthly
Vol. 121, No. 3 (March 2014), pp. 229-236
DOI: 10.4169/amer.math.monthly.121.03.229
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.03.229
Page Count: 8
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Series Involving the Zeta Functions
and a Family of Generalized Goldbach–Euler Series
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Abstract

Abstract We first present the corrected expression for a certain widely-recorded generalized Goldbach–Euler series. The corrected forms are then shown to be connected with the problem of closed-form evaluation of series involving the Zeta functions, which happens to be an extensively-investigated subject since the time of Euler as (for example) in the classical three-century-old Goldbach theorem.

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