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 …

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 …

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 …

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 …

Algebraically, what's happening is that taking an ordinary generating function is a bijection between the vector space of sequences and the ring of formal power series.

Aug 20, 2021 · So I was reading about generating functions and formal power series, and it seems that these two concepts are used interchangeably. Can someone please tell me the …

sequences-and-series combinatorics generating-functions fibonacci-numbers See similar questions with these tags.

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 …

Jun 14, 2024 · Moreover, when you need to ensure convergence, it is to be noted that you are not limited to the standard generating function, but you can consider other types of generating …

1 This is really a too-long comment, not a solution, but I can't resist sharing what the statistician Frederick Mosteller had to say about his first encounter with generating functions. He was …