The Generalized Incomplete Gamma Function as sum over Modified Bessel Functions of the First Kind [PDF]
Journal of Computational and Applied Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
E.J.M. Veling, Veling, E.J.M.
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Inequalities involving modified Bessel functions of the first kind II [PDF]
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 \(v_{p}(x)=2(p+1){{\gamma _{p}(x^{2})}\over {\gamma _{p+1}(x^{2})}}\).
Baricz, Árpád, Neuman, Edward
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Functional inequalities involving Bessel and modified Bessel functions of the first kind [PDF]
Expositiones Mathematicae, 2008 Since the sine and cosine functions and the hyperbolic sine and cosine functions are particular cases of Bessel and modifed Bessel functions, the author extends the inequality \(\cosh x-1\), where \(\Gamma\) is Euler gamma function and \(I_{p}(x)\) is the modified Bessel function of first kind. Some properties and inequalities satisfied by \(G_{p}(x)\)
Baricz, Árpád
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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 J0(r) and the modified Bessel function of the first kind I1(r). The calculus is based on a function of J0(r), I1(r) and of their derivatives, having a Wronskian form. The method here described could be useful for training the students in the manipulation of such integrals.
Sparavigna, Amelia Carolina +1 more
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Inequalities involving modified Bessel functions of the first kind [PDF]
Journal of Mathematical Analysis and Applications, 1992 The author proves some inequalities for modified Bessel functions of the first kind which are related to a log-convexity property of the hypergeometric function \(F_{0,1}(1+\mu;x^ 2/4)\) (\(\mu>-1/2\)).
Neuman, Edward
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Bounds for an integral of the modified Bessel function of the first kind and expressions involving it [PDF]
Journal of Mathematical Analysis and Applications, 2021 18 ...
Robert Gaunt
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Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications [PDF]
Mathematical Inequalities & Applications, 2018 Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ^{2}$ on $\left( 0,\infty \right) $.
Yang, Zhen-Hang, Zheng, Shen-Zhou
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CERTAIN UNIFIED INTEGRAL FORMULAS INVOLVING THE GENERALIZED MODIFIED k-BESSEL FUNCTION OF FIRST KIND [PDF]
Communications of the Korean Mathematical Society, 2017 Generalized integral formulas involving the generalized modified k-Bessel function $J_{k,ν}^{c,γ,λ}\left( z\right) $ of first kind are expressed in terms generalized $k-$Wright functions.
Kottakkaran Sooppy Nisar +1 more
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Journal of Mathematical Chemistry, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yiting Wang, Jing Kong
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On Integral Representation of First Kind Bessel Function [PDF]
, 2004 A first kind Fredholm integral equation with nondegenerate kernel is given, which particular solution is the Bessel function of first kind.
Draščić, Biserka, Pogány, Tibor K
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