Ways of functions with variable period definition and their approximation

Abstract

The ways of analytical definition of functions with variable period have been developed in the article. Their variable periods have been written as well. A problem of functions approximation by trigonometric series has been considered, namely, a method of definition of Fourier coefficients of functions with variable period has been developed. Orthogonal trigonometric system of functions with variable period and its orthogonality interval have been conformed with variable period of the function under research. As an example, for one of the functions the correspondent system of trigonometric functions with variable period has been written, Fourier coefficients have been calculated, a finite Fourier series have been constructed, which analysis has proved the obtained results.