Definition:Second Chebyshev Function/Definition 1

Definition
The second Chebyshev Function $\psi: \R \to \R$ is defined as:
 * $\ds \forall x \in \R: \map \psi x := \sum_{k \mathop \ge 1} \sum_{p^k \mathop \le x} \ln p$

where, for each $k$, the summation extends over all powers of prime numbers $p$ such that $p^k \le x$.

Also see

 * Equivalence of Definitions of Second Chebyshev Function