Proof of the $(\alpha ,\beta )$--inversion formula conjectured by Hsu and Ma

Abstract

In light of the well-known fact that the $n$th divided difference of any polynomial of degree $m$ must be zero while $m<n$,the present paper proves the $(\alpha ,\beta )$-inversion formula conjectured by Hsu and Ma [J. Math. Res. $\&$ Exposition 25(4) (2005) 624]. As applications of $(\alpha ,\beta )$-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.

15 pages

References in corpus (2)

• Summation and transformation formulas for elliptic hypergeometric series
• Summation, transformation, and expansion formulas for multibasic theta hypergeometric series