Second Chebyshev function ($\psi (x)$)

The second Chebyshev function is the summatory Von Mangoldt function, $\psi (x)={\sum }_{n\le x}\Lambda (n)$.

For $x>1$ away from a jump of $\psi$,where the sum over Nontrivial zeros of the Riemann zeta function is taken symmetrically. A finite-height version has an explicit truncation error controlled by $x/T$ and the distance from $x$ to the nearest prime power.