Results 211 to 220 of about 6,388 (244)

Bounds for the product of modified Bessel functions [PDF]

Aequationes Mathematicae, 2016
In this note our aim is to present some monotonicity properties of the product of modified Bessel functions of the first and second kind. Certain bounds for the product of modified Bessel functions of the first and second kind are also obtained.
Saminathan Ponnusamy, Sanjeev Singh, Dragana Jankov Masirevic   +2 more
exaly   +2 more sources

Inequalities involving modified Bessel functions of the first kind II [PDF]

Journal of Mathematical Analysis and Applications, 2007
The intrinsic properties, including logarithmic convexity (concavity), of the modified Bessel functions of the first kind and some other related functions are obtained.
Edward Neuman, Arpad Baricz
exaly   +2 more sources

Inequalities for modified Bessel functions and their integrals [PDF]

Journal of Mathematical Analysis and Applications, 2014
Simple inequalities for some integrals involving the modified Bessel functions Iν(x)Iν(x) and Kν(x)Kν(x) are established. We also obtain a monotonicity result for Kν(x)Kν(x) and a new lower bound, that involves gamma functions, for K0(x)K0(x)
Robert Gaunt
exaly   +2 more sources

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Modified $ q$-Bessel functions and $ q$-Macdonald functions

Sbornik: Mathematics, 1996
Summary: The \(q\)-analogues of modified Bessel functions and Macdonald functions are defined in this paper. As in the case of \(q\)-Bessel functions introduced by Jackson, there are two kinds of these functions. Like their classical prototypes, they arise in harmonic analysis on quantum symmetric spaces.
Ol'shanetskij, M. A., Rogov, V.-B. K.
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On Zeros of the Modified Bessel Function of the Second Kind

Computational Mathematics and Mathematical Physics, 2020
The zeros \(\nu_n\) of the modified Bessel function \(K_{i\nu}(x)\) at \textit{fixed} argument \(x>0\) are shown to be countably infinite and simple. By a suitable transformation of the differential equation satisfied by \(K_{i\nu}(x)\) into a one-dimensional Schrodinger equation with an exponential potential, the equation is expressed as a boundary ...
Bagirova, S. M., Khanmamedov, A. Kh.
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Mathematical Software for Modified Bessel Functions

2014
The high-quality mathematical software for the computation of modified Bessel functions of the second kind with integer, imaginary and complex order and real argument is elaborated. The value of function may be evaluated with high precision for given value of the independent argument x and order r.
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On an integral with modified Bessel function

Journal of Physics A: Mathematical and General, 1991
Using two different methods of calculations of the imaginary part of some Feynman integral (Cutkosky rule and the double transformation), the author obtains a formula \[ \int_ 0^ a I_ 0(z)\cosh \bigl( A\sqrt{a^ 2-z^ 2}\bigr) {{z dz} \over {\sqrt{a^ 2-z^ 2}}}= {{\sinh(a \sqrt{1-A^ 2})} \over {\sqrt{1+A^ 2}}}, \] where \(I_ 0(z)\) is a modified Bessel ...
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On an integral with modified Bessel function

Journal of Physics A: Mathematical and General, 1992
The definite integral over I0(z) evaluated by Bakulev (1991) is shown to be a special case of a tabulated integral.
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Note on Asymptotic Expansions of Modified Bessel Functions

Journal of the Society for Industrial and Applied Mathematics, 1961
In a recent paper the author [1] extended an early result of Stieltjes, as an aid in the calculation of Bessel functions of orders 0 and 1 from their truncated asymptotic expansions. It is the purpose of this short note to extend these results to include modified Bessel functions.
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Rational Bounds for Ratios of Modified Bessel Functions

SIAM Journal on Mathematical Analysis, 1978
Double sequences of rational upper and lower bounds for the ratio ${{I_{\nu + 1} (x)} / {I_\nu (x)}}$, $x > 0$, $\nu > - \frac{1}{2}$ or $\nu > - 1$, are established. The bounds are shown to converge, in certain cases monotonically, to the ratio ${{I_{\nu + 1} (x)} /{I_\nu (x)}}$. A comparison with other approximations is made.
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