For example, most generating functions are actually meromorphic functions, and this means that one can deduce asymptotic information about a sequence from the locations of the poles of its generating …

Jul 20, 2017 · The answer of the question depends on what kind of generating function is used to define the sequence $ (a_n)$. It is not the same an ordinary generating function than an exponential …

Jan 7, 2013 · I'm currently doing a research on generating functions, but I have only found few books on this topic. Can anyone provide references (if possible, trying to assess the level of math competence …

Anyway, now that you hopefully understand roughly what generating functions are, we can turn to their use in counting problems. In general, when we want to find an element of some sequence, one way …

The generating function for the Fibonacci numbers Ask Question Asked 12 years, 9 months ago Modified 1 year, 8 months ago

Nov 25, 2025 · For questions relating to moment-generating-functions (m.g.f.), which are a way to find moments like the mean$~ (μ)~$ and the variance$~ (σ^2)~$. Finding an m.g.f. for a discrete random …

At undergraduate level, it is interesting to work with the moment generating function and state the above theorem without proving it. One possible proof requires familiarity with holomorphic functions and the …

0 The generating function is a power series that is assigned to a sequence. If you have a sequence $\ {a_n|n\in \mathbb N\}$ you can assign to this sequence a power series: $\sum\limits_ {n=0}^\infty …

Generating functions are formed by making a series $\sum_ {n\geq 0} a_n x^n$ out of a sequence $a_n$. They are used to count objects in enumerative combinatorics.

The utility of generating functions goes further than counting-combinatorics. They are a basic tools for dealing with discrete functions, in particular with linear difference equations - and these frequently …