INVERSION RELATIONS AND THE q-RACAH POLYNOMIALS

By the inversion relations given by Andrews, we expand the q shifted factorial (x, gamma delta q/x; q)n in terms of the q-Racah polynomials Rm(mu(x)). As one application of this expansion, we express a 4 phi 3 series as a double sum, from which we derive several Hecke-type identities. As another application, we evaluate the sum ENi=0 omega i center dot Rm(mu(q-i)) center dot (q-i, gamma delta qi+1; q)n by orthogonality, where omega i is the weight function for Rm(mu(x)). This allows us to derive some summation and transformation formulas.