Definition:Second Chebyshev Function/Definition 3

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

where:
 * the summation extends over all prime numbers $p$ such that $p \le x$
 * $\floor {\, \cdot \,}$ denotes the floor function.

Also see

 * Equivalence of Definitions of Second Chebyshev Function