Inequalities for the Landau constants. (Russian) Zbl 0753.41030

Falaleev, L. P.

Sib. Mat. Zh. 32, No. 5(189), 194-195 (1991).

For the Landau constants \(G_ n=\sum^ n_{i=0}\left({(2i)!!\over (2i- 1)!!}\right)^ 2\) the estimation \(1\leq G_ n- {1\over\pi}\ln(n+1)<1.0663\) of L. Brutman [J. Approximation Theory 34, 217-220 (1982; Zbl 0486.41013)] is sharpened by \(1.0662<G_ n- {1\over\pi}\ln(n+3/4)\leq 1.0916\).

Reviewer: L.Berg (Rostock)

MSC:

41A60

Asymptotic approximations, asymptotic expansions (steepest descent, etc.)

Keywords:

Landau constants

Citations:

Zbl 0486.41013