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"Generating Functions" as a book category covers works that develop and apply the theory of power-series representations of sequences and related transform techniques to solve combinatorial, algebraic, analytic, and applied problems. These books typically introduce ordinary and exponential generating functions, formal power series, Dirichlet and Mellin transforms, and core tools such as coefficient extraction, convolution, recurrence solving, Lagrange inversion, and singularity analysis, then show how those tools yield counting formulas, closed forms, asymptotics, and algorithmic solutions. Titles range from rigorous textbooks and reference handbooks to problem collections and applied guides for computer scientists, physicists, and engineers, and often include symbolic/computational methods for manipulating series. Target readers are advanced undergraduates, graduate students, researchers, and practitioners who want systematic techniques for translating discrete problems into analytic ones and extracting quantitative information.

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