Computing with Hypergeometric-Type Terms

Abstract

Take a multiplicative monoid of sequences in which the multiplication is given by Hadamard product. The set of linear combinations of interleaving monoid elements then yields a ring. For hypergeometric sequences, the resulting ring is a subring of the ring of holonomic sequences. We present two algorithms in this setting: one for computing holonomic recurrence equations from hypergeometric-type normal forms and the other for finding products of hypergeometric-type terms. These are newly implemented commands in our Maple package $HyperTypeSeq$, available at \url{https://github.com/T3gu1a/HyperTypeSeq}, which we also describe.