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On approximating the modified Bessel function of the second kind [PDF]
Journal of Inequalities and Applications, 2017 In the article, we prove that the double inequalities π e − x 2 ( x + a ) < K 0 ( x ) < π e − x 2 ( x + b ) , 1 + 1 2 ( x + a ) < K 1 ( x ) K 0 ( x ) < 1 + 1 2 ( x + b ) $$ \frac{\sqrt{\pi}e^{-x}}{\sqrt{2(x+a)}}< K_{0}(x)< \frac{\sqrt{\pi }e^{-x}}{\sqrt ...
Zhen-Hang Yang, Yu-Ming Chu
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Inequalities for the Modified k-Bessel Function
International Journal of Analysis and Applications, 2017 The article considers the generalized k-Bessel functions and represents it as Wright functions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel functions, and the ratio of the k-Bessel and the k-Bessel functions ...
Saiful Rahman Mondal +1 more
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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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Integral Representations for Products of Two Bessel or Modified Bessel Functions [PDF]
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. A similar question for a product of modified Bessel functions of the first kind is solved next, when the input functions are of different integer orders and have different ...
Tibor K Pogány +2 more
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New Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean
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
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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On approximating the modified Bessel function of the first kind and Toader-Qi mean
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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Powers of modified Bessel functions of the first kind
Applied Mathematics Letters, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arpad Baricz
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Amos-type bounds for modified Bessel function ratios.
J Math Anal Appl, 2013 Hornik K, Grün B.
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On Kudriasov Conditions for Univalence of Integral Operators Defined by Generalized Bessel Functions
Mathematics, 2022 In this article, we studied the necessary conditions for the univalence of integral operators that involve two functions: the generalized Bessel function and a function from the well-known class of normalized analytic functions in the open unit disk. The
Mohsan Raza +4 more
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