On the Limit from $q$-Racah Polynomials to Big $q$-Jacobi Polynomials

A limit formula from $q$-Racah polynomials to big $q$-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving ($q$-)Hahn polynomials, little $q$-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey–Wilson to Wilson polynomials and from $q$-Racah to Racah polynomials are given in a more conceptual way.