Abstract
This paper is concerned with extending the list of the known analytical solutions of the pure coalescence equation. Through the use of Laplace transforms three families of exact solutions are obtained for arbitrary initial conditions and for kernels which are certain linear combinations of the constant, sum and product kernels. The solutions which are given in this paper contain, as special cases, the solutions obtained by Scott. Other Special cases of these families of solutions are given for certain initial spectra, namely, the well-known gamma distributions and their limiting function, the Dirac delta function.
