Properties of sums of some elementary functions and their application to computational and modeling problems

The article proposes methods for creating corresponding sums of functions and sums of corresponding series, whose appropriate equations have equal number of solutions. We consider equations composed of power functions (generalized polynomials) and sums of exponential functions. Using the concept of corresponding functions, we prove the relationships between the properties of polynomial, power and sums of exponential functions. One of the results is generalization of Descartes Rule of Signs for sums of other than polynomial functions and sums of their series. Obtained results are applied to two practical problems. One is the finding of an adequate description of transition electrical signals. Secondly, the proved theorems are applied to the problem of finding the initial value for iterative algorithms used to solve one particular case of IRR (internal rate of return) equation for mortgage calculations. Overall, the results are proved to be beneficial for theoretical and practical applications in industry and in different areas of science and technology.