Results 41 to 50 of about 92,603 (214)

Integral Representations for Products of Two Bessel or Modified Bessel Functions [PDF]

Mathematics, 2019
The first part of the article contains integral expressions for products of two Bessel functions of the first kind having either different integer orders or different arguments. A similar question for a product of modified Bessel functions of the first kind is solved next, when the input functions are of different integer orders and have different ...
Dragana Jankov Maširević, Tibor K. Pogány   +1 more
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Note on modified generalized Bessel function

Proyecciones (Antofagasta), 2023
An attempt is made to define Modified Generalized Bessel Function, and Modified Generalized Bessel Matrix Function. Some properties have also been discussed.
Patel, Farhatbanu H., Jana, R. K., Shukla, A. K.   +2 more
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Integral representations for products of two parabolic cylinder functions with different arguments and orders

, 2015
This paper derives new integral representations for products of two parabolic cylinder functions. In particular, expressions are obtained for D_{nu}(x)D_{mu}(y), with x>0 and y>0, that allow for different orders and arguments in the two parabolic ...
Veestraeten, Dirk
core   +1 more source

Non-homogeneous impulsive time fractional heat conduction equation

Journal of Numerical Analysis and Approximation Theory, 2023
This article provides a concise exposition of the integral transforms and its application to singular integral equation and fractional partial differential equations.
Arman Aghili
doaj   +1 more source

On polynomials connected to powers of Bessel functions

, 2013
The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include recurrences in terms of
Moll, Victor H., Vignat, C.
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Bounds and algorithms for the K-Bessel function of imaginary order [PDF]

, 2013
Using the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function${K}_{ir} (x)$of imaginary order and its first two derivatives with respect to the order.
Booker, Andrew R, Strömbergsson, Andreas, Then, Holger L   +2 more
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Asymptotic estimates of the difference of products of Bessel functions by the integral of these functions

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2020
In the study of direct and inverse problems of finding the right-hand side of degenerate equations of mixed type with different boundary conditions, the problem arises of establishing asymptotic estimates for the differences of the products of ...
Kamil Basirovich Sabitov
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Accurate analytic approximation to the Modified Bessel function of Second Kind K 0(x)

Results in Physics, 2022
Two analytic approximations have been determined for the modified Bessel functions of second kind K0(x), good for either positive or negative values of x.
Pablo Martin, Fernando Maass
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Unified Bessel, Modified Bessel, Spherical Bessel and Bessel-Clifford Functions

, 2016
In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K ymaz O. A certain generalized Pochhammer symbol and its applications to hypergeometric functions.
Yaşar, Banu Yılmaz, Özarslan, Mehmet Ali   +1 more
openaire   +2 more sources

Green's function for the lossy wave equation

Revista Brasileira de Ensino de Física
Using an integral representation for the first kind Hankel (Hankel-Bessel Integral Representation) function we obtain the so-called Basset formula, an integral representation for the second kind modified Bessel function.
R. Aleixo, E. Capelas de Oliveira
doaj   +1 more source