Definition:First Chebyshev Function

Definition
The First Chebyshev Function is defined and denoted:


 * $\ds \map \vartheta x := \sum_{p \mathop \le x} \ln p$

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

Also denoted as
Some sources use $\map \theta x$ rather than $\map \vartheta x$.