On the Solutions of Schlömilch's Integral Equations

Year 2017, Volume: 13 Issue: 3, 671 - 676, 30.09.2017

Ahmet Altürk

https://doi.org/10.18466/cbayarfbe.339329

Abstract

The linear Schlömilch's integral equation is an
important and useful equation in atmospheric and terrestrial physics. The
equation and its solution have been used for some ionospheric problems. It can
also be considered as a special type of Fredholm integral equation of the first
kind. This correspondence allows one to use the mathematical tools available
for solving Fredholm integral equation of the first kind. In this article, we
provide an alternative closed-form expression for solutions of the linear and
the nonlinear Schlömilch's integral equation in terms of the well-known gamma
function. Some elaborate examples are provided to demonstrate the simplicity
and applicability of the proposed formulae.

Keywords

Schlömilch’s Integral Equation, Fredholm Integral Equation of the First Kind, Terrestrial Physics, Gamma Function

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