2017/04/10 by Jin Wang, Wang, Jin, Xinrong Ma +1
Mathematics · #05A10 #33D15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #math.CO #msc:05A10 #msc:33D15
paper · pdf · doi:10.48550/arxiv.1704.02695
15 pages
openalex publication_date 2017/04/10 · openalex created_date 2017/04/28 · arxiv created 2020/09/22 · arxiv updated 2020/09/23 · openalex updated_date 2026/07/28
In light of the well-known fact that the nth divided difference of any polynomial of degree m must be zero while m<n,the present paper proves the (α,β)-inversion formula conjectured by Hsu and Ma [J. Math. Res. & Exposition 25(4) (2005) 624]. As applications of (α,β)-inversion, we not only recover some known matrix inversions due to Gasper, Schlosser, and Warnaar, but also fin three new matrix inversions related to elliptic divisibility sequence and theta functions.