CHAPTER 5 - FUNCTIONS DEFINED BY POWER SERIES

Abstract

This chapter discusses the functions defined by power series. A power series is absolutely convergent at all points in the interior of its circle of convergence, and is divergent at all points outside its circle of convergence. The exponential function has a unique inverse function, called the “logarithmic function,” which is increasing, continuous, and differentiable on its domain of definition. The properties of the exponential function help to define the real powers of positive numbers that obey the index laws. These same properties can be used to define complex powers of positive numbers.