# Asymptotics of Multivariate Generating Series

I am new to Sage and I need to find the asymptotic form of the series coefficients of the following generating function:

```
F(t,x,z) = (1 + t*x - t*x*z)/(1 - t - t^2*x - t*x*z + t^2*x*z)
```

In other words, in the Taylor expansion of the function in terms of the variable $t$, I am interested in the asymptotic form of the coefficient of the term $t^L\ x^N\ z^B$ in the limit of large $L$, $N$, and $B$.

Homework ?

I am a Physicist, and a mathematician has helped me to arrive at this generating function for a research problem I am interested in.

Marni Mishna gave a nice course on asymptotics of multivariate generating series in June 2020 during EJCIM2020, see chapter 3 of the EJCIM2020 book (french). The chapter 3 is an excerpt from her recent book Analytic Combinatorics: A Multidimensional Approach.