We propose new two-sided estimates with sharp constants for the number e. Minorants and majorants in the estimates are expressed as continued fractions. To justify the estimate, we essentially use the integral representation of a special analytic function obtained earlier by the authors. We discuss the validity of similar inequalities and relationship with known results.
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Translated from Sirius. Matematicheskii Zhurnal 1, No. 2, 2024 [Accepted]
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Kostin, A.B., Sherstyukov, V.B. Two-Sided Estimates of the Analytic Function Associated with the Euler Number. J Math Sci 284, 83–92 (2024). https://doi.org/10.1007/s10958-024-07329-0
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DOI: https://doi.org/10.1007/s10958-024-07329-0