Asymptotic behavior of the Lagrange points in the Taylor formula (Q1921759)

Let \(\theta_n (x)\) be the least upper bound of the numbers \(\theta\) arrising in the \(n\)-th (last) term in the Taylor expansion of a function \(f\) around 0 and let \(L_n(f) = \liminf_{x\to 0} \theta_n(x)\). The authors have proved the so-called Ionin's conjecture: \(L_n(f) \geq \exp (-(1+ {1\over 2} + {1\over 3} \cdots + {1\over n}))\).