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Inequalities for the Landau constants

✍ Scribed by L. P. Falaleev

Publisher
SP MAIK Nauka/Interperiodica
Year
1992
Tongue
English
Weight
89 KB
Volume
32
Category
Article
ISSN
0037-4466

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## An additive form of the Landau inequality for is proved for 0<c (cos(?Γ‚2n)) &2 , 1 m n&1, with equality for , where T n is the Chebyshev polynomial. From this follows a sharp multiplicative inequality, For these values of \_, the result confirms Karlin's conjecture on the Landau inequality f

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a b s t r a c t Let Ξ³ = 0.577215 . . . be the Euler-Mascheroni constant, and let R n = n k=1 1 2 . This refines the result of D. W. DeTemple, who proved that the double inequality holds with a = 1 and b = 0.