PCs for AP

This month´s column is devoted to the general idea of recursive computation. What is basically involved is expressing an answer for something as a weighted sum of related answers. In computing trigonometric functions, this can take the form of a multiple-angle formula wherein a given function is expressed in terms of functions of related argument. One example is cos[nA] = cos[(n-1)A]cos[A]-sin[(n-1)A]sin[A] . Thus, if A is the angular interval at whicah sequence of cosine functions is required, then having the two starting values cos[A] and sin[A] permits the remaining samples of cos[nA]2,3,..., to be found by recursion. This way of calculating a transcendental function can be more efficient than direction evaluatioonf the function for appropriate problems. Other forms of recursion are used to speed convergence of a sequence of answers, for example when an infinite series is being evaluated numerically. Some examples are given below.