Results 261 to 270 of about 511,370 (297)

(p, q)-Extended Bessel and Modified Bessel Functions of the First Kind

Results in Mathematics, 2017
Inspired by certain recent extensions of the Euler's beta, Gauss hypergeometric and confluent hypergeometric functions [1], we introduce (p, q)- extended Bessel function J_{; ; ; \nu, p, q}; ; ; , the (p, q)- extended modified Bessel function I_{; ; ; ; \nu, p, q}; ; ; ; of the first kind of order \nu by making use two additional parameters in the ...
Jankov Maširević, Dragana, Parmar, Rakesh K., Pogány, Tibor K.   +2 more
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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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Identities associated to a generalized divisor function and modified Bessel function

Research in Number Theory, 2023
D. Banerjee, B. Maji
semanticscholar   +1 more source

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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A new numerical algorithm based on the first kind of modified Bessel function to solve population growth in a closed system

International Journal of Computational Mathematics, 2014
K. Parand, J. Rad, Mehran Nikarya
semanticscholar   +1 more source

Modified Bessel Functions

2019
Julian Schwinger, Lester L. DeRaad, Kimball A. Milton, Wu-yang Tsai   +3 more
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