Hypergeometric series related to the 9-j coefficient of su(1,1)

We study various expressions for the 9-j coefficient of su(1,1), with an emphasis on multiple hypergeometric series. An orthogonal polynomial in two discrete variables is associated to the 9-j coefficient. Some applications are considered, dealing with formulas in which the 9-j coefficient appears as a connection or expansion coefficient, and discussing some transformation formulas for double- and triple-hypergeometric series of unit argument.