Have I found the correct formula? Or is this only numerical aproximation? $\zeta(3)=\frac{2{\pi}^2}{7}(\ln 2-\frac{4}{15})$
Reedited: I add another aproximation(may be better): $\zeta(3)=\frac{2{\pi}^2}{7}(\ln 2-\frac{e\;\pi}{32})$
Just for fun, new one: $$\zeta(3)\dot{=}4\pi^2\left(\ln\left(\frac{16665385931}{9990000}\right)-e^2\right)$$
On
If such a formula were to exist, AND depend on $\pi$, it would be a function of $\pi^3$. But it's unlikely, since the equation of the circle is NOT $x^3+y^3=r^3$. Which is why only even zetas depend on $\pi$.
See Apéry's constant. I think that's just an approximation.