The complete solution of certain diffraction problems can be found in the form of a Sommerfeld integral. To obtain solutions in this form, a kernel must be obtained. There are no doubt, many different techniques for finding them. However, in solving the two‐dimensional problem in a wedge‐shaped region, Malyuzhinets demonstrates that the kernel (except for a periodic factor) is the solution to a difference equation. He gives conditions and proves theorems about this fact. For such problems as he treats, no immediate method is clearly discernible for obtaining the solution of this difference equation. This paper will fill that void.