ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 24 Sep 2020 13:12:38 +0200Asymptotics of Multivariate Generating Serieshttps://ask.sagemath.org/question/53534/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 $B$.Tue, 22 Sep 2020 00:15:05 +0200https://ask.sagemath.org/question/53534/asymptotics-of-multivariate-generating-series/Comment by Mohammad for <p>I am new to Sage and I need to find the asymptotic form of the
series coefficients of the following generating function:</p>
<pre><code>F(t,x,z) = (1 + t*x - t*x*z)/(1 - t - t^2*x - t*x*z + t^2*x*z)
</code></pre>
<p>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 $B$.</p>
https://ask.sagemath.org/question/53534/asymptotics-of-multivariate-generating-series/?comment=53559#post-id-53559I am a Physicist, and a mathematician has helped me to arrive at this generating function for a research problem I am interested in.Wed, 23 Sep 2020 21:56:32 +0200https://ask.sagemath.org/question/53534/asymptotics-of-multivariate-generating-series/?comment=53559#post-id-53559Comment by Sébastien for <p>I am new to Sage and I need to find the asymptotic form of the
series coefficients of the following generating function:</p>
<pre><code>F(t,x,z) = (1 + t*x - t*x*z)/(1 - t - t^2*x - t*x*z + t^2*x*z)
</code></pre>
<p>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 $B$.</p>
https://ask.sagemath.org/question/53534/asymptotics-of-multivariate-generating-series/?comment=53565#post-id-53565Marni Mishna gave a nice course on asymptotics of multivariate generating series in June 2020 during [EJCIM2020](https://ejcim2020.sciencesconf.org/), see chapter 3 of the [EJCIM2020 book (french)](https://www.labri.fr/perso/vpenelle/ejcim.pdf). The chapter 3 is an excerpt from her recent book [Analytic Combinatorics: A Multidimensional Approach](https://www.bookshare.org/browse/book/2966893).Thu, 24 Sep 2020 11:32:22 +0200https://ask.sagemath.org/question/53534/asymptotics-of-multivariate-generating-series/?comment=53565#post-id-53565Comment by Emmanuel Charpentier for <p>I am new to Sage and I need to find the asymptotic form of the
series coefficients of the following generating function:</p>
<pre><code>F(t,x,z) = (1 + t*x - t*x*z)/(1 - t - t^2*x - t*x*z + t^2*x*z)
</code></pre>
<p>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 $B$.</p>
https://ask.sagemath.org/question/53534/asymptotics-of-multivariate-generating-series/?comment=53550#post-id-53550Homework ?Wed, 23 Sep 2020 21:00:00 +0200https://ask.sagemath.org/question/53534/asymptotics-of-multivariate-generating-series/?comment=53550#post-id-53550Answer by tmonteil for <p>I am new to Sage and I need to find the asymptotic form of the
series coefficients of the following generating function:</p>
<pre><code>F(t,x,z) = (1 + t*x - t*x*z)/(1 - t - t^2*x - t*x*z + t^2*x*z)
</code></pre>
<p>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 $B$.</p>
https://ask.sagemath.org/question/53534/asymptotics-of-multivariate-generating-series/?answer=53567#post-id-53567You can have a look at the corresponding documentation: https://doc.sagemath.org/html/en/reference/asymptotic/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.html
Do not hesitate to ask if you are locking somewhere, by explaining what you tried, what did or did not work, etc.
Thu, 24 Sep 2020 13:12:38 +0200https://ask.sagemath.org/question/53534/asymptotics-of-multivariate-generating-series/?answer=53567#post-id-53567