Summary: A differential method for recovering a function \(f(t_1,t_2)\) from its two-dimensional Laplace-Carson transform \(pq\widehat f(p,q)\) given as continuous or discrete data on a finite interval is presented. The introduction of the variables \(u_1=\frac1p\), \(u_2=\frac1q\) converts this transform into a Mellin convolution, with a transformed kernel involving the gamma function. The truncation of the infinite product representation of \(\frac{1}{\Gamma(1-s)\Gamma(1-w)}\) leads to an approximate differential expression for the solution.