Abstract
This article researches the approach to solving different instances of Cauchy integral equations by utilizing the Lucas polynomial technique. The technique decreases the solution of a specified singular integral equation to the solution of an array equation corresponding to a linear scheme of algebraic equations with unnamed Lucas coefficients. An evaluation of the introduced strategy has been described. Some numerical illustrates are introduced to display the accuracy and efficiency of the suggested strategy. The comparison between the results which are obtained by the Lucas polynomial method and other methods such as the Lerch polynomial method, Chebyshev polynomial method, Bernstein polynomial method, and the reproducing kernel method is represented in a group of tables. All the numerical results are obtained by using the Maple 18 program.