Computing with Hypergeometric-Type Terms

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. We consider such a construction for the monoid of hypergeometric sequences, yielding what we call the ring of hypergeometric-type sequences -- 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 $\texttt{HyperTypeSeq}$, which we also describe.