ABSTRACT
The generating functions constitute an important means for a unied
treatment of combinatorial and probabilistic problems. P. S. Laplace, their
inventor, has rst introduced them in the form of power series. Later,
generating functions of a more general than the power series form have
been used. Moreover, for their combinatorial uses, they are to be regarded,
following E. T. Bell, as tools in the study of an algebra of sequences; thus,
despite all appearances they belong to algebra and not to analysis.
