my question is, let us suppose we can find an expansion for the prime number (either exact or approximate)(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \pi (x) = \sum _{n=0}^{\infty}a_n log(x) [/tex]

and we have the expression for the logarithmic integral

[tex] Li (x) = \sum _{n=0}^{\infty}b_n log(x) [/tex]

where the numbers a(n) and b(n) are known , then my question is , what could one expect about the difference expansion

[tex] \pi (x) - Li(x) = \sum _{n=0}^{\infty}(a_n - b_n) log(x) [/tex] ??

**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!

# Expansion for the prime counting function

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