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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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(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 Bessel function asymptotics via probability

Statistics & Probability Letters, 1987
Let the modified Bessel function be defined by \[ I_{\rho}(x)=\sum^{\infty}_{k=0}\frac{1}{k!}\frac{1}{\Gamma (k+\rho +1)}(x/2)^{2k+\rho}\quad for\quad \rho \geq -1\quad and\quad -\infty
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Asymptotic approximations for modified Bessel functions

Journal of Mathematical Physics, 1980
The behavior of a qν(x) =Iν(x)/Iνa(x), where Iν is a modified Bessel function with integral or half-integral index ν and Iνa the leading term of its asymptotic series, is investigated for x≫1. It is shown that qν(x) may be approximated by eν(x) =exp(−ν2/2x), the difference rν(x) =qν(x)−eν(x) being of order x−1/4.
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Riemann xi function and modified Bessel functions

St. Petersburg Mathematical Journal
In a recent paper the author constructed a canonical system of differential equations with a diagonal Hamiltonian related to the Riemann zeta function. With this system an integral representation in terms of modified Bessel functions is associated for elements of the de Branges space related to the canonical system.
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Chimeric antigen receptor T‐cell therapy in multiple myeloma: A comprehensive review of current data and implications for clinical practice

Ca-A Cancer Journal for Clinicians, 2023

exaly  

Definite Integrals involving Modified Bessel Functions

          In this paper, we develop fifteen definite integral involving Modified Bessel function of first kind. Furthermore, we also develop the generalized formula for the same using Inspection method.
M.P. Chaudhary, Salah Uddin, Amresh Yadav, Hervé Wendpagnagdé Ouedraogo   +3 more
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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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Modified Bessel Functions

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