Introduction to Analytic Number Theory
《Introduction to Analytic Number Theory》 · 第 75 页 · Section 4.2「Chebyshev's functions $\psi(x)$ and $\vartheta(x)$」，Definitions
Chebyshev's functions are defined by $\psi(x)=\sum_{n\le x}\Lambda(n)$ and $\vartheta(x)=\sum_{p\le x}\log p$, where $p$ runs over the primes not exceeding $x$.