Abstract
This chapter presents a study of the different kinds of series that are widely used as generating functions. It discusses formal power series. Operations on formal series involve corresponding operations on their coefficients. If the series actually converge and represent functions, operations on those functions correspond to certain operations on the power series coefficients of the expansions of those functions. The chapter explores a few of these relationships. It also discusses the calculus of formal exponential generating functions and reviews the basic analytic properties of power series and their coefficient sequences. Generating functionologists need reference lists of known power series and other series that occur frequently in applications of the theory. The chapter presents a list of some useful power series. For each series, it shows the series and its sum. It also discusses another kind of generating function that matches yet another kind of convolution of two sequences, a kind that also occurs naturally in many problems in combinatorics and number theory.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.