Generating Functions in Engineering and the Applied Sciences

Sequences often become easier to study when they can be expressed as functions. Generating Functions in Engineering and the Applied Sciences introduces that idea and follows it into the kinds of problems encountered in mathematics, engineering, statistics, and other applied fields. Its emphasis is practical breadth: readers meet familiar generating functions, newer forms, and examples of how the methods travel across disciplines.

From sequences to useful functions

The book introduces ordinary, exponential, and probability generating functions, among other commonly used forms. It also presents Pochhammer generating functions for rising and falling factorials. The approach is intended to give readers a foundation in the techniques without assuming prior study of discrete mathematics or combinatorics.

New perspectives on discrete distributions

Two of the book’s distinctive topics are the mean deviation generating function and the survival function generating function. The authors use the mean deviation generating function to derive mean deviations for a range of discrete distributions, bringing generating-function methods into a statistical setting.

Applications across disciplines

The closing chapter surveys uses in areas such as algebra, analysis of algorithms, combinatorics, graph theory, number theory, reliability, epidemiology, bioinformatics, genetics, polymer chemistry, management, economics, and statistics. This cross-disciplinary view helps connect the mathematical techniques to varied subject areas rather than leaving them as isolated definitions.

A useful starting point for applied study

Students and practitioners in engineering and applied sciences may find this introduction helpful when generating functions appear in their courses or work. Readers interested in combinatorial mathematics or statistical applications will also find topics that extend beyond the most familiar ordinary and exponential forms.