ABSTRACT
Understanding of infinite series is necessary to comprehend analytic functions. Integrals in the complex plane, like the real integrals of elementary calculus, are the limits of sums, and this chapter concerns limits. MATLAB® can be a useful tool in determining how rapidly a sequence of functions approaches its limit—if indeed it has one. A finite portion of an infinite series can be a useful device for approximating not only an analytic function but also an integral, and a numerical comparison employing MATLAB can be useful to investigate the validity of approximations. Infinite series, as a means of approximating functions, do have their limitations, and sometimes infinite products are preferable. The concepts, sums and limits, provide the basis for understanding the most important and common operation in complex variable theory: contour integration. MATLAB provides a wealth of methods for integration.
