Is the author uses another reference for this result.

Question

In this page: https://en.wikipedia.org/wiki/Chebyshev_function#Asymptotics_and_bounds

The author write the inequality: $$|ψ(x)-x|≤0.006409(x/log x)$$ for $x≥e²²$.

But when looking to the original source: Rosser, J. Barkley; Schoenfeld, Lowell (1962). "Approximate formulas for some functions of prime numbers". Illinois J. Math. 6: 64–94. (https://projecteuclid.org/download/pdf_1/euclid.ijm/1255631807)

I cannot find this inequality.

My question is: Is the author uses another reference for this result.

Answer 1

The Wikipedia article cites multiple sources; the right one is:

Pierre Dusart, Sharper bounds for $\psi, \theta, \pi, p_k$, Rapport de recherche no. 1998-06, Université de Limoges.

It is Theorem 3 on page 6.