caa a22 4500 463178203 CHVBK 20180406164831.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s11139-006-0257-x doi (NATIONALLICENCE)springer-10.1007/s11139-006-0257-x Ruijsenaars S. Centre for Mathematics and Computer Science, P.O. Box 94079, 1090 GB, Amsterdam, The Netherlands aut Quadratic transformations for a function that generalizes 2F1 and the Askey-Wilson polynomials [Elektronische Daten] [S. Ruijsenaars] In previous papers we introduced and studied a ‘relativistic' hypergeometric function R(a +, a −, c; v, $$\hat{V}$$ ) that satisfies four hyperbolic difference equations of Askey-Wilson type. Specializing the family of couplings c∊ $$\mathbb{C}^4$$ to suitable two-dimensional subfamilies, we obtain doubling identities that may be viewed as generalized quadratic transformations. Specifically, they give rise to a quadratic transformation for 2 F 1 in the ‘nonrelativistic' limit, and they yield quadratic transformations for the Askey-Wilson polynomials when the variables v or $$\hat{V}$$ are suitably discretized. For the general coupling case, we also study the bearing of several previous results on the Askey-Wilson polynomials. Springer Science + Business Media, LLC, 2006 Relativistic hypergeometric function nationallicence Quadratic transformations nationallicence Askey-Wilson difference operators nationallicence Askey-Wilson polynomials nationallicence Parameter shifts nationallicence The Ramanujan Journal Kluwer Academic Publishers 13/1-3(2007-06-01), 339-364 1382-4090 13:1-3<339 2007 13 11139 https://doi.org/10.1007/s11139-006-0257-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-006-0257-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ruijsenaars S. Centre for Mathematics and Computer Science, P.O. Box 94079, 1090 GB, Amsterdam, The Netherlands aut NATIONALLICENCE 773 0- The Ramanujan Journal Kluwer Academic Publishers 13/1-3(2007-06-01), 339-364 1382-4090 13:1-3<339 2007 13 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer