Definition:First Chebyshev Function

Definition
The First Chebyshev Function $\vartheta \left({x}\right)$, or $\theta \left({x}\right)$, is defined as:


 * $\displaystyle \vartheta \left({x}\right) = \sum_{p \le x} \ln p$

where the sum extends over all prime numbers $p$ such that $p \le x$.