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## Main Question or Discussion Point

Is there any reliable way to convert a series to a product, or the opposite? I was looking at the following and wanted to know more:

[tex]\sum_{n=1}^{\infty}\frac{1}{n^{s}}=\prod_{p}\left(1-p^{-s}\right)^{-1}[/tex]

[tex]\sum_{n=1}^{\infty}\frac{1}{n^{s}}=\prod_{p}\left(1-p^{-s}\right)^{-1}[/tex]