Some limit relations in the \(A_{1}\) tableau of Dunkl-Cherednik operators (Q1432893)

The author studies some limit relations involving some \(q\)-special functions related with the \(A_{1}\) root system tableau of Dunkl-Cherednik operators. In particular, he studies the limit relations involving the \(q\)-ultraspherical polynomials, the \(q\)-Hermite and the Hermite polynomials. He considers the limit transitions of non-symmetric analogues of the special families of orthogonal polynomials, as the limit transitions for the usual families are well-known. The limit results obtained in this paper complete the \(A_{1}\) classification of \(q\)-basic polynomials.