Fractional-Modified Bessel Function of the First Kind of Integer Order
Mathematics, 2023 The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas.
Andrés Martín, Ernesto Estrada
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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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New Sharp Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean [PDF]
Mathematics, 2020 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
Zhen-Hang Yang +2 more
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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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An integral containing a Bessel Function and a Modified Bessel Function of the First Kind [PDF]
, 2017 Here we discuss the calculation of an integral containing the Bessel function J_0(r) and the modified Bessel function of the first kind I_1(r). The calculus is based on a function of J_0(r), I_1(r) and of their derivatives, having a Wronskian form.
Amelia Carolina Sparavigna
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On approximating the modified Bessel function of the first kind and Toader-Qi mean [PDF]
Journal of Inequalities and Applications, 2016 In the article, we present several sharp bounds for the modified Bessel function of the first kind I 0 ( t ) = ∑ n = 0 ∞ t 2 n 2 2 n ( n ! ) 2 $I_{0}(t)=\sum_{n=0}^{\infty}\frac{t^{2n}}{2^{2n}(n!)^{2}}$ and the Toader-Qi mean T Q ( a , b ) = 2 π ∫ 0 π ...
Zhen-Hang Yang, Yu-Ming Chu
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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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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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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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Correction to: Geometric Properties of the Products of Modified Bessel Functions of the First Kind [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khaled Mehrez, Sourav Das, Anish Kumar
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