Main achievements of function theory with variable period have been described. The tasks aimed at their further study, namely the task of functions with variable period “approximation” Fourier series, and development the appropriate information technologies of their analysis have been emphasized. To make the investigation of the methods of function study with variable period testing possible different ways of analytical definition of such functions have been developed. Formulae of finding Fourier coefficients of the function with variable period have been recorded and the principles of Fourier series theory have been established.