Generalization of the Laplace Transform of Powers of the sinc function

Abstract

In this work, general expressions are found for the Laplace transform of \[L\left(\frac{\sin^m(at)}{t^n}\right) \quad \text{or} \quad L\left(\frac{\sin^n(t)\,\sin^m(at)}{t^p}\right).\] The results are expressed in terms of usual functions such as logarithms, arctangent, and rational functions. Thus, these expressions can be incorporated into the general literature to facilitate the calculation of Laplace transforms. In addition, the results of the article can be implemented in different mathematical software for a direct calculation of such transforms or to study the analytical properties of these transforms more directly.