  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.
