The Solution of the Modified Helmholtz Equation in a Wedge and an Application to Diffusion-Limited Coalescence

The general solution of the modified Helmholtz equation, q_{xx}(x,y)+q_{yy}(x,y)-4b^2q(x,y)=0, in the wedge 0 < x < y < infinity, is presented. This solution is used to find the explicit steady-state of diffusion-limited coalescence, A+A<-->A, on the half-line, with a trap-source at the origin.