Two Finite Forms of Watson's Quintuple Product Identity and Matrix Inversion

Abstract

Recently, Chen-Chu-Gu and Guo-Zeng found independently that Watson's quintuple product identity follows surprisingly from two basic algebraic identities, called finite forms of Watson's quintuple product identity. The present paper shows that both identities are equivalent to two special cases of the $q$-Chu-Vandermonde formula by using the ($f,g$)-inversion.