Definition:Second Chebyshev Function/Definition 3
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Definition
The second Chebyshev Function $\psi: \R \to \R$ is defined as:
- $\ds \forall x \in \R: \map \psi x := \sum_{p \mathop \le x} \floor {\log_p x} \ln p$
where:
- the summation extends over all prime numbers $p$ such that $p \le x$
- $\floor {\, \cdot \,}$ denotes the floor function.
Also see
Source of Name
This entry was named for Pafnuty Lvovich Chebyshev.