On Qi’s Normalized Remainder of Maclaurin Power Series Expansion of Logarithm of Secant Function

In the study, the authors introduce Qi’s normalized remainder of the Maclaurin power series expansion of the function lnsecx=−lncosx; in view of a monotonicity rule for the ratio of two Maclaurin power series and by virtue of the logarithmic convexity of the function (2x−1)ζ(x) on (1,∞), they prove...

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Veröffentlicht in:Axioms 2024-12, Vol.13 (12), p.860
Hauptverfasser: Zhang, Hong-Chao, Guo, Bai-Ni, Du, Wei-Shih
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Sprache:eng
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Zusammenfassung:In the study, the authors introduce Qi’s normalized remainder of the Maclaurin power series expansion of the function lnsecx=−lncosx; in view of a monotonicity rule for the ratio of two Maclaurin power series and by virtue of the logarithmic convexity of the function (2x−1)ζ(x) on (1,∞), they prove the logarithmic convexity of Qi’s normalized remainder; with the aid of a monotonicity rule for the ratio of two Maclaurin power series, the authors present the monotonic property of the ratio between two Qi’s normalized remainders.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13120860