Some infinite sums arising from the Weierstrass product theorem

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• 作者：Istvá ; n Mez? ^{istvan.mezo@epn.edu.ec}
• 关键词：Digamma function ; Trigamma function ; Hurwitz zeta function ; Prime zeta function ; Generalized harmonic numbers ; Weierstrass product theorem
• 刊名：Applied Mathematics and Computation
• 出版年：2013
• 出版时间：15 May, 2013
• 年：2013
• 卷：219
• 期：18
• 页码：9838-9846
• 全文大小：349 K

文摘

A very simple approach using series manipulations and the Weierstrass Representation Theorem yield surprisingly nice and non-trivial series identities involving special functions. In our paper we present a large number of examples of these identities. At the end, several number theoretical sums are deduced.