Results 181 to 190 of about 496,864 (207)

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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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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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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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  

Bell polynomials and modified Bessel functions of half-integral order

Applied Mathematics and Computation, 2015
P. Natalini, P. Ricci
semanticscholar   +1 more source

Modified Bessel Functions

1997
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Inequalities for modified Bessel functions and their integrals

Journal of Mathematical Analysis and Applications, 2014
Robert E Gaunt
exaly  

Modified Bessel Functions

1986
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