AsyRec: A Maple package for Computing the
Asymptotics of Solutions of Linear Recurrence Equations
with Polynomial Coefficients
By Doron Zeilberger
.pdf
.ps
.tex
(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger)
Written: April 4, 2008.
This is a short paper that describes a much longer Maple package, that
should have accompanied my 1985 article with Jet Wimp
Resurrecting the asymptotics of linear recurrences, J. Math. Anal. Appl. v. 111, 162177 (1985).
That article was not a very good resurrection, since we used pencilandpaper
and only got the leading terms. Now with Maple, we can do so much more.
IMPORTANT: this article accompanies a much more important object, the
Maple program
AsyRec
, that uses the BirkhoffTrjitznisky method to compute asymptotics of solutions
of homogeneus linear recurrence equations with polynomial coefficients.
Sample Input and Output

To get the asymptotics for the number of permutations whose rth power is the
identity permutation, for r from 2 to 6,
the
input
yields
the output.

To get the asymptotics for the sums of powers of the binomial coefficients,
up to the 8th power, the
input
yields
the output.

To get the asymptotics for the famous Apery numbers, the
input
yields
the output.
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
Doron Zeilberger's Home Page