AsyRec: A Maple package for Computing the Asymptotics of Solutions of Linear Recurrence Equations with Polynomial Coefficients

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.
Last updates of this page: Oct. 11, 2024.
Previous updates of this page: April 26, 2016.
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 Maple program AsyRec.txt , 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, the
input yields the output.

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

To get the asymptotics for the famous Apery numbers, the
input yields the output.

Added Oct. 11, 2024, to celebrate Neil Sloane's 85th birthday:
To get the asymptotics for the famous number of involutions OEIS sequence A85
the input yields the output.

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
Doron Zeilberger's Home Page