Polynomial Reduction for Holonomic Sequences

Rong-Hua Wang, Michael X. X. Zhong

Published 2022-05-23Version 1

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 $\pi$-series involving Domb numbers and Franel numbers.