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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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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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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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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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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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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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.
Baricz, Árpád, Mehrez, Khaled
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Convexity of ratios of the modified Bessel functions of the first kind with applications
Revista Matemática Complutense, 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 ...
Zhen-Hang Yang, Jing-Feng Tian
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On the cumulative distribution function of the variance-gamma distribution [PDF]
, 2023 We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From these formulas, we
Gaunt, Robert E.
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