New Sharp Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 02 Jun 2020 English Publisher:MDPI AGJournal:Mathematics, volume 8, page 901 (eissn: 2227-7390,

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Authors: Zhen-Hang Yang; Jing-Feng Tian; Ya-Ru Zhu;

doi: 10.3390/math8060901

New Sharp Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean

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Abstract

Let I v x be he modified Bessel function of the first kind of order v. We prove the double inequality sinh t t cosh 1 / q q t < I 0 t < sinh t t cosh 1 / p p t holds for t > 0 if and only if p ≥ 2 / 3 and q ≤ ln 2 / ln π . The corresponding inequalities for means improve already known results.

Related Organizations

North China Electric Power University
China (People's Republic of)

Keywords

inequality, QA1-939, modified Bessel function of the first kind, hyperbolic function, mean, Mathematics

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