Results 201 to 210 of about 80,976 (233)

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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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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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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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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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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Monotonicity and inequalities involving the modified Bessel functions of the second kind

Journal of Mathematical Analysis and Applications, 2022
Zhen-Hang Yang, Yu-Ming Chu
exaly  

Monotonicity of Three Classes of Functions Involving Modified Bessel Functions of the Second Kind

Bulletin of the Iranian Mathematical Society, 2023
Jing-Feng Tian
exaly  

Convexity and concavity of the modified Bessel functions of the first kind with respect to Hölder means

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2020
Tie-Hong Zhao, Yu-Ming Chu
exaly