Extension of the parameter range of the power series expressions and asymptotes of the exact solutions to Smoluchowski's coagulation equation with gamma distributions as initial size spectra

In order to obtain a wide set of test cases for numerical methods to solve Smoluchowski's coagulation equation the exact solutions for the constant, sum or product kernel, with gamma distributions as initial size spectra, are generalized by allowing size distributions with a singularity at zero volume.