Definition:First Chebyshev Function

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


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

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