Abstract
Theory of analytic functions is one of major fields of modern mathematics. Its application covers broad range of topics of natural science. A complex function f (z), or a function that takes a complex number z as a variable, has various properties that often differ from those of functions that take a real number x as a variable. In particular, the analytic functions hold a paramount position in the complex analysis. In this chapter we explore various features of the analytic functions accordingly. From a practical point of view, the theory of analytic functions is very frequently utilized for the calculation of real definite integrals. For this reason, we describe the related topics together with tangible examples.
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