The Dawson Transform and its Applications

Some properties of the Dawson Integral are presented first in the current work, followed by the introduction of the Dawson Integral Transform. Iteration identities and relationships, similar to the Parseval Goldstein type, are established involving various well-known integral transforms, such as the Laplace Transform, the L 2 -Transform, and the Dawson Integral for the new integral transform. Furthermore, improper integrals of well-known functions, including the Dawson Integral, Exponential Integral, and the Macdonald Function, are evaluated using the results obtained.