scholarly journals Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones

2018 ◽  
Vol 141 (4) ◽  
pp. 474-500 ◽  
Author(s):  
Margit Rösler ◽  
Michael Voit
Keyword(s):  
Bessel Functions ◽  
Symmetric Cones ◽  
Beta Distributions

SERIES EXPANSIONS OF THE GENERALIZED K-BESSEL FUNCTIONS ON SYMMETRIC CONES

2008 ◽  
Vol 06 (01) ◽  
pp. 1-10 ◽  
Author(s):  
HONGMING DING ◽  
WEI HE
Keyword(s):  
Series Expansion ◽  
Bessel Functions ◽  
Series Expansions ◽  
Symmetric Cones ◽  
Expansion Formula

In this paper, we generalize the series expansion formula of classical K-Bessel functions to symmetric cones.

scholarly journals Some Applications of the Wright Function in Continuum Physics: A Survey

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 198
Author(s):  
Yuriy Povstenko
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Exponential Function ◽  
Nonlocal Elasticity ◽  
Bessel Functions ◽  
Wright Function ◽  
Mainardi Function ◽  
Integral Relations

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed.

scholarly journals On Subclasses of Uniformly Spiral-like Functions Associated with Generalized Bessel Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
B. A. Frasin ◽  
Ibtisam Aldawish
Keyword(s):  
Integral Operator ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Bessel Functions ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind zup(z) to be in the classes SPp(α,β) and UCSP(α,β) of uniformly spiral-like functions and also give necessary and sufficient conditions for z(2-up(z)) to be in the above classes. Furthermore, we give necessary and sufficient conditions for I(κ,c)f to be in UCSPT(α,β) provided that the function f is in the class Rτ(A,B). Finally, we give conditions for the integral operator G(κ,c,z)=∫0z(2-up(t))dt to be in the class UCSPT(α,β). Several corollaries and consequences of the main results are also considered.

scholarly journals A new product formula involving Bessel functions

2021 ◽  
pp. 1-17
Author(s):  
Mohamed Amine Boubatra ◽  
Selma Negzaoui ◽  
Mohamed Sifi
Keyword(s):  
Bessel Functions ◽  
New Product ◽  
Product Formula

scholarly journals Dispersive Estimates for Full Dispersion KP Equations

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Didier Pilod ◽  
Jean-Claude Saut ◽  
Sigmund Selberg ◽  
Achenef Tesfahun
Keyword(s):  
Stationary Phase ◽  
Initial Value Problem ◽  
Bessel Functions ◽  
Linear Part ◽  
Independent Interest ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Initial Value ◽  
Kp Equations ◽  
Well Posed

AbstractWe prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev–Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev–Petviashvili equations. The proof of these estimates combines the stationary phase method with sharp asymptotics on asymmetric Bessel functions, which may be of independent interest. As a consequence, we prove that the initial value problem associated to the Full Dispersion Kadomtsev–Petviashvili is locally well-posed in $$H^s(\mathbb R^2)$$ H s ( R 2 ) , for $$s>\frac{7}{4}$$ s > 7 4 , in the capillary-gravity setting.

scholarly journals Accurate analytic approximation for the Chapman grazing incidence function

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Dmytro Vasylyev
Keyword(s):  
Asymptotic Expansion ◽  
Radiative Transfer ◽  
Bessel Functions ◽  
Grazing Incidence ◽  
Analytical Approximation ◽  
Analytic Approximation ◽  
Atmospheric Physics ◽  
Uniform Asymptotic Expansion ◽  
Grazing Angles ◽  
Physical And Chemical

AbstractA new analytical approximation for the Chapman mapping integral, $${\text {Ch}}$$ Ch , for exponential atmospheres is proposed. This formulation is based on the derived relation of the Chapman function to several classes of the incomplete Bessel functions. Application of the uniform asymptotic expansion to the incomplete Bessel functions allowed us to establish the precise analytical approximation to $${\text {Ch}}$$ Ch , which outperforms established analytical results. In this way the resource consuming numerical integration can be replaced by the derived approximation with higher accuracy. The obtained results are useful for various branches of atmospheric physics such as the calculations of optical depths in exponential atmospheres at large grazing angles, physical and chemical aeronomy, atmospheric optics, ionospheric modeling, and radiative transfer theory.

Sign in / Sign up

Export Citation Format

Share Document