  We solve a weakly singular integral equation by Laplace transformation over a
finite interval of R. The equation is transformed into a Cauchy integral
equation, whose resolution amounts to solving two Fredholm integral equations
of the second kind with regular kernels. This classical scheme is used to
clarify the emergence of the auxiliary functions expressing the solution of the
problem. There are four such functions, two of them being classical ones. This
problem is encountered while studying the propagation of light in strongly
scattering media such as stellar atmospheres.
