Summation of functional series by method of finite hybrid integral transform of Fourier.
by
Andriy Blazhievskiy
Khmelnitskiy Institute of RM&Law

There are many engineering problems, which occur in design and calculation of the stability of machine constructive elements, in the designing engineer structure and in the research of kinetic of physical and chemical processes.

Since the constructive elements are under action of instantaneous heat-stroke and after they work in stationary state, someone would like to know the value of the stationary heat strength. This problem is very important with respect to composite materials. The stationary state of a system is described by the functions depending on functional series consisting of the combination of trigonometric and Bessel functions. Since it is easier for us to deal with functions than with series, we encounter the problem of the function series summation.

By the Cauchy's method for the separate systems of the ordinary differential equations, we have constructed the solution of the corresponding boundary problem in the case of general assumption on the differential and connected operators. The condition of the non-limited solving and the structure of the general solution for the boundary problem is written in the explicit form. On the other hand the solution of this problems has been constructed by the method of the finite hybrid integral transforms. Since We know that this problem has one and only one solution, we may compare the first solution with the second and, as a result, get the sums of functional series. My research is devoted to the summation of just such series by the method of finite hybrid integral transforms

Date received: March 5, 1999