# 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 $B$.

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Homework ?

( 2020-09-23 14:00:00 -0500 )edit

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

( 2020-09-23 14:56:32 -0500 )edit

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.

( 2020-09-24 04:32:22 -0500 )edit

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You can have a look at the corresponding documentation: https://doc.sagemath.org/html/en/refe...

Do not hesitate to ask if you are locking somewhere, by explaining what you tried, what did or did not work, etc.

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