The divided difference operator introduced by R. Askey and J. Wilson [Mem. Am. Math. Soc. 319, 55 p. (1985; Zbl 0572.33012)] plays the same role for the \({}_ 4\phi_ 3\) orthogonal polynomials that the derivative does for Jacobi polynomials. This article gives a nice derivation of the connection coefficient result of L. J. Rogers [Proc. Lond. Math. Soc. 26, 15-32 (1895)] using this divided difference operator.