Abstract

This chapter presents integral transforms under which Laplace transform, Fourier transform, Fourier sine and cosine transforms, and Mellin transform are discussed, followed by their basic properties. In addition, a table of Laplace transform pairs, Fourier transform pairs, Fourier transform pairs for spherically symmetric functions, and Mellin cosine transforms is also illustrated. The Fourier transform is also called the exponential or complex Fourier transform of the function f(x) and denoted by F(ξ). The Fourier sine and cosine transforms of the function f(x) are denoted by Fs (ξ) and Fc (ξ) respectively.

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