The identification problem for transcendental functions

Abstract

In this article algorithmic methods are presented that have essentially been introduced into computer algebra systems like Mathematica within the last decade. The main ideas are due to Stanley and Zeilberger. Some of them had already been discovered in the last century by Beke, but because of their complexity the underlying algorithms have fallen into oblivion. We combined these ideas, and added a factorization algorithm in noncommutative rings (Melenk--Koepf \cite{MK}) leading to a solution of the identification problem for a large class of transcendental functions. We present implementations of these algorithms in computer algebra systems.