TY - JOUR
ID - 85170
TI - A variant of van Hoeij's algorithm to compute hypergeometric term solutions of holonomic recurrence equations
JO - Journal of Algorithms and Computation
JA - JAC
LA - en
SN - 2476-2776
AU - Teguia Tabuguia, Bertrand
AD - Department of Mathematics and Natural Sciences, University of Kassel, Heinrich-Plett-Str. 40., Kassel, Germany
Y1 - 2021
PY - 2021
VL - 53
IS - 2
SP - 1
EP - 32
DO - 10.22059/jac.2021.85170
N2 - Linear and homogeneous recurrence equations having polynomial coefficients are said to be holonomic. These equations are useful for proving and discovering combinatorial and hypergeometric identities. Given a field $\mathbb{K}$ of characteristic zero, $a_n$ is a hypergeometric term with respect to $\mathbb{K}$, if the ratio $a_{n+1}/a_n$ is a rational function over $\mathbb{K}$. Two algorithms by Marko Petkov\v{s}ek (1993) and Mark van Hoeij (1999) were proposed to compute hypergeometric term solutions of holonomic recurrence equations. The latter algorithm is more efficient and was implemented by its author in the Computer Algebra System (CAS) Maple through the command \texttt{LREtools[hypergeomsols]}. We describe
a variant of van Hoeij's algorithm that performs with the same efficiency without considering certain recommendations of the original version. We implemented our algorithm in the CASes Maxima and Maple. It also appears for some particular cases that our code finds results where \texttt{LREtools[hypergeomsols]} fails.
Our implementation is part of the \texttt{FPS} software which can be downloaded at \url{http://www.mathematik.uni-kassel.de/~bteguia/FPS_webpage/FPS.htm}. The command is \texttt{HypervanHoeij} for Maxima 5.44 and \texttt{rectohyperterm} for Maple 2021.
UR - https://jac.ut.ac.ir/article_85170.html
L1 - https://jac.ut.ac.ir/article_85170_fb0789d8c397ce9d958fbd9c4cdaf5eb.pdf
ER -