Two-Sided Estimates of the Analytic Function Associated with the Euler Number

Two-Sided Estimates of the Analytic Function Associated with the Euler Number

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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.284 (1), p.83-92
Hauptverfasser: Kostin, A. B., Sherstyukov, V. B.
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Estimates
Mathematics
Mathematics and Statistics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07329-0