Inequalities for the Landau constants.(Russian)Zbl 0753.41030

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.)

Landau constants

Zbl 0486.41013
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