Results 51 to 60 of about 49,816 (162)

Functional inequalities involving Bessel and modified Bessel functions of the first kind

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 \(G_{p}(x)\)
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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.
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On polynomials connected to powers of Bessel functions

, 2013
The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include recurrences in terms of
Moll, Victor H., Vignat, C.
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Inequalities involving modified Bessel functions of the first kind

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 \(F_{0,1}(1+\mu;x^ 2/4)\) (\(\mu>-1/2\)).
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Mehler-Heine asymptotics for multiple orthogonal polynomials

, 2016
Mehler-Heine asymptotics describe the behavior of orthogonal polynomials near the edges of the interval where the orthogonality measure is supported. For Jacobi polynomials and Laguerre polynomials this asymptotic behavior near the hard edge involves ...
Van Assche, Walter
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On an identity for zeros of Bessel functions

, 2014
In this paper our aim is to present an elementary proof of an identity of Calogero concerning the zeros of Bessel functions of the first kind. Moreover, by using our elementary approach we present a new identity for the zeros of Bessel functions of the ...
Baricz, Árpád, Maširević, Dragana Jankov, Pogány, Tibor K., Szász, Róbert   +3 more
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Analysis of ( P , m ) $(P,\mathrm{m})$ -superquadratic function and related fractional integral inequalities with applications

Journal of Inequalities and Applications
In the present work we establish for the first time a class of ( P , m ) $(P,\mathrm{m})$ -superquadratic functions and look into its features. Using them, we come up with the Jensen and Hermite–Hadamard inequalities, as well as the fractional versions ...
Dawood Khan, Saad Ihsan Butt, Youngsoo Seol   +2 more
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Inequalities for integrals of the modified Struve function of the first kind

, 2018
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant.
Gaunt, Robert E.
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Remarks on a parameter estimation for von Mises--Fisher distributions

, 2013
We point out an error in the proof of the main result of the paper of Tanabe et al. (2007) concerning a parameter estimation for von Mises--Fisher distributions, we correct the proof of the main result and we present a short alternative proof.Comment: 3 ...
Baricz, Árpád
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Some special functions and cylindrical diffusion equation on α-time scale

Demonstratio Mathematica
This article is dedicated to present various concepts on α\alpha -time scale, including power series, Taylor series, binomial series, exponential function, gamma function, and Bessel functions of the first kind.
Silindir Burcu, Tuncer Zehra, Gergün Seçil, Yantir Ahmet   +3 more
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