Chebyshev function

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In mathematics, the Chebyshev function is either a scalarising function (Tchebycheff function) or one of two related functions. The first Chebyshev function ϑ(x) or θ(x) is given by ϑ ( x ) = ∑ p ≤ x log ⁡ p {\displaystyle \vartheta (x)=\sum _{p\leq x}\log p} where log {\displaystyle \log } denotes the natural logarithm, with the sum extending over all prime numbers p that are less than or equal to x. The second Chebyshev function ψ(x) is defined similarly, with the sum extending over all prime powers not exceeding x ψ ( x ) = ∑ k ∈ N ∑...

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