# EVALUATION OF CERTAIN ALTERNATING SERIES

• Choi, Junesang (Department of Mathematics, Dongguk University)
• Accepted : 2014.01.28
• Published : 2014.06.25
• 127 39

#### Abstract

Ever since Euler solved the so-called Basler problem of ${\zeta}(2)=\sum_{n=1}^{\infty}1/n^2$, numerous evaluations of ${\zeta}(2n)$ ($n{\in}\mathbb{N}$) as well as ${\zeta}(2)$ have been presented. Very recently, Ritelli [61] used a double integral to evaluate ${\zeta}(2)$. Modifying mainly Ritelli's double integral, here, we aim at evaluating certain interesting alternating series.

#### Keywords

Riemann Zeta function;Basler problem;Bernoulli numbers;double integrals;residue theorem

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