Expansion formulas for terminating balanced 4F3-series from the Biedenharn–Elliot identity for su(1,1)

In a recent paper, George Gasper (Contemp. Math. 254 (2000) 187) proved some expansion formulas for terminating balanced hypergeometric series of type 4F3 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 3F2-series. We conclude with some basic analogues and show their relation with the Askey–Wilson polynomials.