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

Zhen-Hang Yang, Jing-Feng Tian and Ya-Ru Zhu
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Zhen-Hang Yang: Engineering Research Center of Intelligent Computing for Complex Energy Systems of Ministry of Education, North China Electric Power University, Yonghua Street 619, Baoding 071003, China
Jing-Feng Tian: Department of Mathematics and Physics, North China Electric Power University, Yonghua Street 619, Baoding 071003, China
Ya-Ru Zhu: Department of Mathematics and Physics, North China Electric Power University, Yonghua Street 619, Baoding 071003, China

Mathematics, 2020, vol. 8, issue 6, 1-13

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.

Keywords: modified Bessel function of the first kind; hyperbolic function; mean; inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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