scholarly journals Analytic Approximation of Matrix Functions

2003 ◽  
pp. 565-684
Author(s):  
Vladimir Peller
Keyword(s):  
Analytic Approximation ◽  
Matrix Functions

scholarly journals Analytic approximation of matrix functions in Lp

2009 ◽  
Vol 158 (2) ◽  
pp. 242-278 ◽  
Author(s):  
L. Baratchart ◽  
F.L. Nazarov ◽  
V.V. Peller
Keyword(s):  
Analytic Approximation ◽  
Matrix Functions

scholarly journals Analytic approximation of rational matrix functions

2007 ◽  
Vol 56 (4) ◽  
pp. 1913-1937 ◽  
Author(s):  
V. V. Peller ◽  
V. I. Vasyunin
Keyword(s):  
Analytic Approximation ◽  
Matrix Functions ◽  
Rational Matrix

Extended Bessel Matrix Functions

2018 ◽  
Vol 6 (1) ◽  
pp. 1-11
Author(s):  
Ayman SHEHATA
Keyword(s):  
Matrix Functions

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.

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