Most of the functions encountered in introductory analysis belong to the class of elementary functions. This class is composed of polynomials, rational functions, transcendental functions (trigonometric, exponential, logarithmic, and so on), and functions constructed by combining two or more of these functions through addition, subtraction, multiplication, division, or composition. Beyond these functions lies a class of special functions which are important in a variety of engineering and physics applications.
The use of integral transforms is heavily interlaced with special functions like the gamma function, error function, Bessel functions, and so forth. Also, functions such as the Heaviside unit function and the impulse function, which are employed in a variety of engineering applications, are briefly discussed. Hence, a brief review of (or introduction to) some of these special functions can be quite useful before discussing integral transforms themselves.
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