Quadratic transformations for a function that generalizes \(_{2}F_{1}\) and the Askey-Wilson polynomials (Q2369916)

Using the relativistic hypergeometric functions \(R(a_+,a_-,\mathbf{c},v,\hat{v})\) (for definitions see e.g. [\textit{S. N. M. Ruijsenaars}, ``A relativistic hypergeometric function'', J. Comput. Appl. Math. 178, No. 1--2, 393--417 (2005; Zbl 1077.33001)], which are the solution of four hyperbolic difference equations of the Askey-Wilson type, the authors obtain several new quadratic transformation formulas for the Askey-Wilson polynomials.