AsyRec: A Maple package for Computing the
Asymptotics of Solutions of Linear Recurrence Equations
with Polynomial Coefficients
By Doron Zeilberger
(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, 162-177 (1985).
That article was not a very good resurrection, since we used pencil-and-paper
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
, that uses the Birkhoff-Trjitznisky 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 r-th power is the
identity permutation, for r from 2 to 6,
To get the asymptotics for the sums of powers of the binomial coefficients,
up to the 8-th power, the
To get the asymptotics for the famous Apery numbers, the
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
Doron Zeilberger's Home Page