Results 21 to 30 of about 49,816 (162)
An integral containing a Bessel Function and a Modified Bessel Function of the First Kind
, 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.
Amelia Carolina Sparavigna
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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.
Árpád Baricz, Khaled Mehrez
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Inequalities involving modified Bessel functions of the first kind II
Journal of Mathematical Analysis and Applications, 2006 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 \(v_{p}(x)=2(p+1){{\gamma _{p}(x^{2})}\over {\gamma _{p+1}(x^{2})}}\).
Árpád Baricz, Edward Neuman
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Inequalities for integrals of modified Bessel functions and expressions involving them
Journal of Mathematical Analysis and Applications, 2018 Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits.
Gaunt, Robert E.
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Inequalities for an integral involving the modified Bessel function of the first kind [PDF]
Simple bounds are obtained for the integral $\int_0^x\mathrm{e}^{-\gamma t}t^\nu I_\nu(t)\,\mathrm{d}t$, $x>0$, $\nu>-1/2$, $0\leq\gamma0$, $\nu>-1/2$, $0\leq\gamma-1/2$. We complement this upper bound with several other upper and lower bounds that are tight as $x\rightarrow0$ or as $x\rightarrow\infty$, and apply our results to derive sharper bounds ...
Robert E. Gaunt
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The Generalized Incomplete Gamma Function as sum over Modified Bessel Functions of the First Kind
Journal of Computational and Applied Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
E. J. M. Veling
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Journal of Computational and Applied Mathematics, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Els Coussement, Walter Van Assche
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Journal of Mathematical Chemistry, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yi‐Ting Wang, Jing Kong
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Efficient Calculation of Modified Bessel Functions of the First Kind, $I_ν (z)$, for Real Orders and Complex Arguments: Fortran Implementation with Double and Quadruple Precision [PDF]
We present an efficient self-contained algorithm for computing the modified Bessel function of the first kind $I_ν(z)$, implemented in a robust Fortran code supporting double and quadruple (quad) precision. The algorithm overcomes the limitations of Algorithm 644, which is restricted to double precision and applies overly conservative underflow and ...
Mofreh R. Zaghloul, Steven G. Johnson
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Computer Modeling in Engineering & Sciences, 2021 Hong Yan, Bai‐Ni Guo, Feng Qi
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