2022/05/23 by Ronghua Wang, Wang, Rong-Hua, Michael X. X. Zhong +1 · 1 citation
Computer Science · Mathematics · #05A10 #05A19 #11B65 #11B83 #33F10 #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2205.11129
openalex publication_date 2022/05/23 · openalex created_date 2022/06/30 · openalex updated_date 2026/07/28
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 π-series involving Domb numbers and Franel numbers.