Transformation formulas for double hypergeometric series related to 9-j coefficients and their basic analogs

In a recent paper, Alisauskas deduced different triple sum expressions for the 9-j coefficient of su(2) and su(q)(2). For a singly stretched 9-j coeff icient, these reduce to different double sum series. Using these distinct s eries, we deduce a set of new transformation formulas for double hypergeome tric series of Kampe de Feriet type and their basic analogs. These transfor mation formulas are valid for rather general parameters of the series, alth ough a common feature is that all the series appearing here are terminating . It is also shown that the transformation formulas deduced here generate a group of transformation formulas, thus yielding an invariance group or sym metry group of particular double series. (C) 2001 American Institute of Phy sics.