Chebyshev theta function
From specialfunctionswiki
The Chebyshev $\vartheta$ function is $$\vartheta(x) = \displaystyle\sum_{p \leq x} \log p,$$ where $p \leq x$ denotes that $p$ is a prime number less than the real number $x$ and $\log$ denotes the logarithm.
Plot of $\vartheta$ on $[0,50]$.
Plot of $\vartheta$ on $[0,100]$.
Plot of $\vartheta$ on $[0,1000]$.
