Ask Your Question
1

Asymptotics of Multivariate Generating Series

asked 2020-09-22 00:15:05 +0100

Mohammad gravatar image

updated 2020-09-24 01:41:44 +0100

slelievre gravatar image

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 $B$.

edit retag flag offensive close merge delete

Comments

Homework ?

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 2020-09-23 21:00:00 +0100 )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.

Mohammad gravatar imageMohammad ( 2020-09-23 21:56:32 +0100 )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.

Sébastien gravatar imageSébastien ( 2020-09-24 11:32:22 +0100 )edit

1 Answer

Sort by » oldest newest most voted
0

answered 2020-09-24 13:12:38 +0100

tmonteil gravatar image

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.

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2020-09-22 00:15:05 +0100

Seen: 271 times

Last updated: Sep 24 '20