Talk:Zeroes of Gamma Function

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The proof is incorrect/incomplete, since $a_n \neq 0$, $a_n \rightarrow 1$ does not in general imply $\prod_{n\geq 1} a_n \neq 0$. Counter-example: Let $a_n := \exp(-\frac{1}{n})$. Then $a_n \neq 0$ for $n \geq 1$, $a_n \rightarrow 1$, but $\prod_{n \geq 1} a_n = 0$. --Rigla (talk) 14:54, 30 January 2013 (UTC)