In mathematics, the big q-Jacobi polynomials Pn(x;a,b,c;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.[1]
Definition
editThe polynomials are given in terms of basic hypergeometric functions by
References
edit- ^ Andrews, George E.; Askey, Richard (1985), "Classical orthogonal polynomials", in Brezinski, C.; Draux, A.; Magnus, Alphonse P.; Maroni, Pascal; Ronveaux, A. (eds.), Polynômes orthogonaux et applications. Proceedings of the Laguerre symposium held at Bar-le-Duc, October 15–18, 1984., Lecture Notes in Math, vol. 1171, Berlin, New York: Springer-Verlag, pp. 36–62, doi:10.1007/BFb0076530, ISBN 978-3-540-16059-5, MR 0838970
Further reading
edit- 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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