Following Euler if we define the product:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] (x-2^{-s})(x-3^{-s}) (x-5^{-s})(x-7^{-s}).......=f(x) [/tex]

taken over all primes and s > 1 ,what would be the value of f(x) ?? i believe that [tex] f(x,s)=1/Li_{s} (x) [/tex] (inverse of Polylogarithm) however i'm not 100 % sure, although for x=1 you get the inverse of Riemann Zeta

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Is this product convergent

**Physics Forums | Science Articles, Homework Help, Discussion**