Solution of a diffusion of dust problem in terms of hypergeometric functions (Q1381779)

The problem of transport of a heavy pollutant (dust) in an infinite stripe \(0\leq x\leq L\) with an arbitrary initial distribution (at \(x=L\)) has been considered by I. Ali and the first author in another paper (to appear). By using an integral representation of the solution of an analogous problem previously treated by \textit{M. Ye. Berlyand} [Problems of atmospheric diffusion and pollution. Leningrad (1975)], the pollutant concentration for \(x>L\) is here obtained (in closed form) in terms of the confluent hypergeometric function of two variable \(\Phi_1 (a,b;c;x,y)\).