Chebyshev function




In mathematics, the Chebyshev function is either of two related functions. The first Chebyshev function ϑ(x) or θ(x) is given by
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: