Monotonicity of the ratio of modified Bessel functions of the first kind with applications [PDF]
Journal of Inequalities and Applications, 2018 Let Wv(x)=xIv(x)/Iv+1(x) $W_{v} ( x ) =xI_{v} ( x ) /I_{v+1} ( x ) $ with Iv $I_{v}$ be the modified Bessel functions of the first kind of order v. In this paper, we prove the monotonicity of the function x↦(Wv(x)−p)2−(2v+2−p)2x2 $$ x\mapsto\frac{ ( W_{v}
Zhen-Hang Yang, Shen-Zhou Zheng
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Convexity of ratios of the modified Bessel functions of the first kind with applications. [PDF]
Rev Mat Complut, 2022 Let I ν x be the modified Bessel function of the first kind of order ν . Motivated by a conjecture on the convexity of the ratio W ν x = x I ν x / I ν + 1 x for ν > - 2 , using the monotonicity rules for a ratio of two power series and an elementary technique, we present fully the convexity of the functions W ν x , W ν x - x 2 / 2 ν + 4 ...
Yang ZH, Tian JF.
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Arithmetic Means for a Class of Functions and the Modified Bessel Functions of the First Kind [PDF]
Mathematics, 2019 In the paper, by virtue of the residue theorem in the theory of complex functions, the authors establish several identities between arithmetic means for a class of functions and the modified Bessel functions of the first kind, present several identities ...
Feng Qi, Shao-Wen Yao, Bai-Ni Guo
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The logarithmic concavity of modified Bessel functions of the first kind and its related functions [PDF]
Advances in Difference Equations, 2019 This research demonstrates the log-convexity and log-concavity of the modified Bessel function of the first kind and the related functions. The method of coefficient is used to verify such properties.
Thanit Nanthanasub +2 more
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New Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean [PDF]
Mathematics, 2021 Let Ipx be the modified Bessel function of the first kind of order p. The upper and lower bounds in the form of simple rational functions about cosht and (sinht)/t for the function I0x are obtained.
Ling Zhu
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Redheffer type bounds for Bessel and modified Bessel functions of the first kind [PDF]
Aequationes Mathematicae, 2018 In this paper our aim is to show some new inequalities of Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series.
Arpad Baricz, Khaled Mehrez
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Integral Representations for Products of Two Bessel or Modified Bessel Functions
Mathematics, 2019 The first part of the article contains integral expressions for products of two Bessel functions of the first kind having either different integer orders or different arguments.
Dragana Jankov Maširević +1 more
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Inequalities involving modified Bessel functions of the first kind II
Journal of Mathematical Analysis and Applications, 2007 The paper deals with the modified Bessel function of the first kind and order \(p\), denoted by \(I_{p}(x)\), \(x\in R\), \(p\neq -1,-2,\dots\) and the functions \(\mathcal{I}_{p}(x)=2^{p}\Gamma (p+1)x^{-p}I_{p}(x)\), \(\gamma _{p}(x)=\mathcal{I}_{p}(\sqrt{x})\) and \(v_{p}(x)=2(p+1){{\gamma _{p}(x^{2})}\over {\gamma _{p+1}(x^{2})}}\).
Arpad Baricz, Edward Neuman
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Redheffer type inequalities for modified Bessel functions
Arab Journal of Mathematical Sciences, 2016 In this short note, we give new proofs of Redheffer’s inequality for modified Bessel functions of first kind published by Ling Zhu (2011). In addition, using the Grosswald formula we prove new Redheffer type inequality for the modified Bessel functions ...
Khaled Mehrez
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Geometric Nature of the Turánian of Modified Bessel Function of the First Kind
AxiomsThis work explores the geometric properties of the Turanian of the modified Bessel function of the first kind (TMBF). Using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starlikeness, convexity,
Samanway Sarkar +3 more
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