Chapter 8 Advanced Topics in the Theory of Functions

Abstract

By 1880 the main features of the present-day complex function theory had been created, although not assembled into their modern order. Cauchy and Riemann were dead, but Weierstrass was in firm control of his own version of the theory and lecturing on it as part of his 2-year cycle of lectures in Berlin. As we saw in the previous chapter, complex function theory in its various forms had found in widening number of successful applications to other domains of both pure and applied mathematics. In this chapter we look at how the ideas of the founders led to important developments in the theory of complex functions itself and to the discovery of some of the central features of complex function theory as a rich research topic in its own right.