On the equivalence of representations of Green’s functions of boundary value problems for the fractional diffusion equation

In this paper, formulas for the integral Stankovich transforms of some elementary and special functions that are important in the theory of boundary value problems of mathematical physics are obtained. To prove the obtained formulas, integral representations, or expansions in power series, of the functions to which the transforms are applied are usedIn this paper, proves the equivalence of two expansions in series in some special functions. This paper is a continuation of the previously proven equivalence of two forms of the Green function of the first boundary value problem in a rectangular domain for the fractional diffusion equation.