Definition:Second Chebyshev Function/Definition 2

Definition
The second Chebyshev Function $\psi: \R \to \R$ is defined as:
 * $\ds \forall x \in \R: \map \psi x := \sum_{1 \mathop \le n \mathop \le x} \map \Lambda n$

where $\Lambda$ is the von Mangoldt function.

Also see

 * Equivalence of Definitions of Second Chebyshev Function