A CLASS OF DIRICHLET PROBLEMS FOR THE HELMHOLTZ-EQUATION

A formal solution is obtained to a class of Dirichlet problems for Hel mholtz's equation within a corner. It is shown that, for corner angles p pi/q, where p and a are relatively prime integers, the expansions o f the solutions in the neighbourhood of the corner include a term prop ortional to r(q) In(r), where r is the distance from the corner. A suf ficient condition to ensure the absence of such terms is given.