Sharp bounds of the Landau constants

Mortici, Cristinel

doi:10.1090/S0025-5718-2010-02428-7

Sharp bounds of the Landau constants

Author: Cristinel Mortici
Journal: Math. Comp. 80 (2011), 1011-1018
MSC (2010): Primary 41A60; Secondary 26D15
DOI: https://doi.org/10.1090/S0025-5718-2010-02428-7
Published electronically: October 25, 2010
MathSciNet review: 2772106
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Abstract: The aim of this paper is to establish new bounds of the Landau constants.

References

Horst Alzer, On some inequalities for the gamma and psi functions, Math. Comp. 66 (1997), no. 217, 373–389. MR 1388887, DOI https://doi.org/10.1090/S0025-5718-97-00807-7
Horst Alzer, Inequalities for the constants of Landau and Lebesgue, J. Comput. Appl. Math. 139 (2002), no. 2, 215–230. MR 1876636, DOI https://doi.org/10.1016/S0377-0427%2801%2900426-5
L. Brutman, A sharp estimate of the Landau constants, J. Approx. Theory 34 (1982), no. 3, 217–220. MR 654287, DOI https://doi.org/10.1016/0021-9045%2882%2990011-9
Djurdje Cvijović and Jacek Klinowski, Inequalities for the Landau constants, Math. Slovaca 50 (2000), no. 2, 159–164. MR 1763118
L. P. Falaleev, Inequalities for Landau constants, Sibirsk. Mat. Zh. 32 (1991), no. 5, 194–195, 210 (Russian); English transl., Siberian Math. J. 32 (1991), no. 5, 896–897 (1992). MR 1155818, DOI https://doi.org/10.1007/BF00971190

E. Landau, Abschätzung der Koeffzientensumme einer Potenzreihe, Arch. Math. Phys. 21 (1913), 42–50, 250–255.

G.N. Watson, The constants of Landau and Lebesgue, Quart. J. Math. Oxford Ser. 1 (2) (1930), 310–318.

Dejun Zhao, Some sharp estimates of the constants of Landau and Lebesgue, J. Math. Anal. Appl. 349 (2009), no. 1, 68–73. MR 2455731, DOI https://doi.org/10.1016/j.jmaa.2008.08.035