In a recent paper, George Gasper (Contemp. Math. 254 (2000) 187) proved some expansion formulas for terminating balanced hypergeometric series of type 4 F 3 with unit argument. In this article we show how one easily derives such expansion formulas from the Biedenharn–Elliot identity for the Lie algebra su(1,1) . Furthermore, we give a rather systematic method for determining when two apparently different expansion formulas are the same up to transformation formulas. This is a rather nice application of the so-called invariance groups of hypergeometric series. The method extends to other cases; we briefly indicate how it works in the case of expansion formulas for 3 F 2-series. We conclude with some basic analogues and show their relation with the Askey–Wilson polynomials.