Big q-Jacobi polynomials

The polynomials are given in terms of basic hypergeometric functions by

${\displaystyle \displaystyle P_{n}(x;a,b,c;q)={}_{3}\phi _{2}(q^{-n},abq^{n+1},x;aq,cq;q,q)}$

• Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 96 (2nd ed.), Cambridge University Press, ISBN 978-0-521-83357-8, MR 2128719
• Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), "9.8 Jacobi", Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, pp. 216–221, doi:10.1007/978-3-642-05014-5, ISBN 978-3-642-05013-8, MR 2656096 gives a detailed list of properties.
• Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F. (2010), "Chapter 18: Orthogonal Polynomials", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.

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