In his famous article Riemann about Zeta hypothesis start from the Euler's product and rewrite it as an integral. Can someone explain me how this passage is done, because, it's evident for the great Riemann but not for me …in other word how Riemann does to pass from the first to the second equation?
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1You should write down which formulas you are talking about. – Aphelli Mar 17 '21 at 10:23
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yes i would but i didn't manage to do it. i'm not able to use well yet those Tex tools. Maybe i can insert https://fr.wikisource.org/wiki/Sur_le_nombre_de_nombres_premiers_inférieurs_àune_taille_donnée(Riemann,_trad._Laugel). It's about the 2 first formula.. how he get it ? – Doubop Facehell Jazzfunk Mar 17 '21 at 11:18
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The two equations aren’t really related. They’re both “elementary” facts. Note that we nowadays call $\Gamma(s)$ the function that Riemann calls $\Pi(s-1)$. – Aphelli Mar 17 '21 at 11:58
