Using the Long Functional Series in Technical Systems and Increasing Their Efficiency Due to Recurrent Formulae

One of the main areas of training for a modern technical systems engineer is complex automation. Analysis of the functioning of automation systems, their design is carried out using the so-called typical effects, that is, signals with known parameters. In a large number of cases, complex effects can be represented as power functions of time. In some cases, such series can reach a large number of terms. And this is not the only example in engineering practice when the approximation of some processes is realized through expansions into long functional series. It is a mistake to believe that the speeds of modern processors are so high that they can free the programmer from the sometimes-difficult search for recurrent formulas and confine them to programming the sum of a series, based on a ready-made formula for the general term of the series. The aim of this study is to show that the use of recurrent relations not only allows to increase the speed of calculations, but is often the only condition for obtaining the correct final result. The codes of programs presented in the article that implement the processing of a series by two methods and a comparison of their results are quite convincing evidence of the need to search for and use recurrent relations in the development of algorithms based on the use of various types of series.