Polinomios de Rogers

Los polinomios de Rogers se pueden definir en términos de los símbolos q-Pochhammer y de la serie hipergeométrica básica por

${\displaystyle C_{n}(x;\beta |q)={\frac {(\beta ;q)_{n}}{(q;q)_{n}}}e^{in\theta }{}_{2}\phi _{1}(q^{-n},\beta$ ;\beta ^{-1}q^{1-n};q,q\beta ^{-1}e^{-2i\theta })}

donde x = cos(θ).

• Askey, Richard; Ismail, Mourad E. H. (1983), «A generalization of ultraspherical polynomials», en Erdős, Paul, ed., Studies in pure mathematics. To the memory of Paul Turán., Basel, Boston, Berlin: Birkhäuser, pp. 55-78, ISBN 978-3-7643-1288-6, MR 820210.
• Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, Encyclopedia of Mathematics and its Applications 96 (2nd edición), Cambridge University Press, ISBN 978-0-521-83357-8, MR 2128719.
• Macdonald, I. G. (2003), Affine Hecke algebras and orthogonal polynomials, Cambridge Tracts in Mathematics 157, Cambridge University Press, ISBN 978-0-521-82472-9, MR 1976581, doi:10.1017/CBO9780511542824.
• Rogers, L. J. (1892), «On the expansion of some infinite products», Proc. London Math. Soc. 24 (1): 337-352, JFM 25.0432.01, doi:10.1112/plms/s1-24.1.337.
• Rogers, L. J. (1893), «Second Memoir on the Expansion of certain Infinite Products», Proc. London Math. Soc. 25 (1): 318-343, doi:10.1112/plms/s1-25.1.318.
• Rogers, L. J. (1894), «Third Memoir on the Expansion of certain Infinite Products», Proc. London Math. Soc. 26 (1): 15-32, doi:10.1112/plms/s1-26.1.15.