Methods for discriminating convergence and divergence of an improper integral was utilized to analysis the convergence and divergence of the representation formula of solutions of polyharmonic equations boundary value problem,The concrete formula of the equation was given in certain restricted conditions,The corresponding integral expressions were studied,Furthermore,the power of functions was divided into three parts in real number field and the convergence and divergence of corresponding integral expressions were analyzed separately in each section,Based on the above discussion,the study shows that the integral expressions of solutions are convergent if the power is greater than a certain critical value and the singularity is removable,while they are divergent if the power is less than the critical value and the singularity is nonremovable.