An approach to the zero recognition problem by Buchberger algorithm (Q1199821)

This paper has two purposes. The first is to present an algorithm to obtain differential equations for a definite integral with parameters, which is based on the Buchberger algorithm [cf. \textit{B. Buchberger} and \textit{R. Loos}, Computing Suppl. 4, 11-43 (1982; Zbl 0494.68045)]. The second purpose is to improve \textit{D. Zeilberger's} zero recognition method [J. Comput. Appl. Math. 32, No. 3, 321-368 (1990; Zbl 0738.33001)]\ for holonomic functions by the first algorithm. The author presents conjectures and open problems concerning the ``correctness'' of the algorithm.