In the present age, when computers are applied almost anywhere in science, engineering and, indeed, all around us in day-to-day life, it becomes more and more important to implement mathematical functions for efficient evaluation in computer programs. It is usually necessary for this purpose to use all kinds of ‘approximations’ of functions rather than their exact mathematical form. There are various reasons why this is so. A simple one is that in many instances it is not possible to implement the functions exactly, because, for instance, they are only represented by an infinite expansion. Furthermore, the function we want to use may not be completely known to us, or may be too expensive or demanding of computer time and memory to compute in advance, which is another typical, important reason why approximations are required. This is true even in the face of ever increasing speed and computer memory availability, given that additional memory and speed will always increase the demand of the users and the size of the problems which are to be solved. Finally, the data that define the function may have to be computed interactively or by a step-by-step approach which again makes it suitable to compute approximations. With those we can then pursue further computations, for instance, or further evaluations that are required by the user, or display data or functions on a screen.