Polyharmonic functions in structures of exact solutions in the elasticity theory

We introduce an asymptotic algorithm that allows us to construct both approximate and exact solutions to a set of equations in the linear elasticity theory. The exact solutions are expressed by polynomials in one of coordinates, while their coefficients include polyharmonic functions that dependent on two other coordinates. For the sake of ordering of solutions, one can associate every exact solution with the number of the asymptotic approximation.