Computing with Hypergeometric-Type Terms
<|reference_start|>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.<|reference_end|>
@article{tabuguia2024computing,
    title={Computing with Hypergeometric-Type Terms},
    author={Bertrand Teguia Tabuguia},
    journal={arXiv preprint arXiv:2404.10143},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10143},
    primaryClass={cs.SC cs.DM cs.MS}
}