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Sharp bounds for the Landau constants

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Abstract

The Landau constants are defined for all integers n≥0 by

$$ G_{n}=\sum_{k=0}^{n} \frac{1}{16^k}\binom{2k}{k}^2. $$

We establish sharp bounds for the Landau constants G n . Relevant connections of the results presented here with those derived in earlier work are also pointed out.

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Acknowledgements

The numerical calculations presented in this work were performed by using the Maple software for symbolic computations.

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Authors and Affiliations

  1. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, 454003, Henan Province, China

    Chao-Ping Chen

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  1. Chao-Ping Chen
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Correspondence to Chao-Ping Chen.

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Chen, CP. Sharp bounds for the Landau constants. Ramanujan J 31, 301–313 (2013). https://doi.org/10.1007/s11139-012-9436-0

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  • DOI: https://doi.org/10.1007/s11139-012-9436-0

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