Integral relations for special functions of hypergeometric and Heun class

Ordinary differential equations with polynomial coefficients originate different kinds of integral relations for its solutions: integral representations in terms of simpler functions, integral equations etc. In this paper, a new kind of integral relations for functions of the Heun class are presented. These relations are coupling in ivolution eigensolutions, which are characterized by different behaviour at singularities and often also by different intervals of consideration and equations themselves. The studied relations are arranged in two staircases where each succeeding equation may be obtained with the help of the confluence process.