Polynomial reduction for holonomic sequences and applications in $\pi$-series and congruences
Combinatorics
2022-06-28 v2 Number Theory
Abstract
Polynomial reduction, designed first for hypergeometric terms, can be used to automatically prove and generate new hypergeometric identities from old ones. In this paper, we extend the reduction method to holonomic sequences. As applications, we describe an algorithmic way to prove and generate new multi-summation identities. Especially we present new families of -series involving Domb numbers and Franel numbers.
Keywords
Cite
@article{arxiv.2205.11129,
title = {Polynomial reduction for holonomic sequences and applications in $\pi$-series and congruences},
author = {Rong-Hua Wang and Michael X. X. Zhong},
journal= {arXiv preprint arXiv:2205.11129},
year = {2022}
}