The same modest result can be obtained by looking through the standard textbooks on complex analysis for concrete functions. In all three example classes mentioned, we actually do not need any additional theory to deal with the functions, we can derive them directly without complex analysis, i.e. without using the theorems of that theory: we only need to extend the usual justifications of real analysis to complex arguments. Historically, (i) and (ii) as well as the essential parts of (iii) were known by the beginning of the 19th century. It was not until the 19th century that complex analysis began to triumph in analysis, when a theory had to be developed to deal with new classes of functions. Such a class of functions is examined in Chapter I.