Integral equations and potential-theoretic type integrals of orthogonal polynomials

Abelʹs theorem is used to solve the Fredholm integral equations of the first kind with Gaussʹs hypergeometric kernel. The case that the kernel takes general form is discussed in detail and the solution is given. Here, the works of some authors are considered as special cases. The discussion focuses on the three dimensional contact problems in the theory of elasticity with general kernel.