I found a reference to the following article ;
O B Sheynin, The appearance of Dirac's delta functions in the works of P S Laplace (Russian), Istor.-Mat. Issled. Vyp. 20 (1975), 303-308, 381.
I don't have access to this nor can I read in Russian. Can anyone summarize this paper? I'm fairly familiar with the Laplace and other integral transforms, so a brief statement of and explanation of any nonstandard notation in the central formula or formulas as presented by Laplace would probably suffice.