Definition:Second Chebyshev Function/Definition 1
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Definition
The second Chebyshev Function $\psi: \R \to \R$ is defined as:
- $\ds \forall x \in \R: \map \psi x := \sum_{k \mathop \ge 1} \sum_{p^k \mathop \le x} \ln p$
where, for each $k$, the summation extends over all powers of prime numbers $p$ such that $p^k \le x$.
Also see
Source of Name
This entry was named for Pafnuty Lvovich Chebyshev.