罗杰斯多项式

罗杰斯多项式又称连续q超球面多项式是一个以超几何函数定义的超几何正交多项式[1]

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

其中 x = cos(θ).即 $\theta =arccos(x)$

极限关系

${\displaystyle P_{n}(cos\phi$

ROGERS POLYNOMIALS ABS COMPLEX3D MAPLE PLOT

ROGERS POLYNOMIALS IM COMPLEX3D MAPLE PLOT

ROGERS POLYNOMIALS RE COMPLEX3D MAPLE PLOT

ROGERS POLYNOMIALS ABS DENSITY MAPLE PLOT

ROGERS POLYNOMIALS IM DENSITY MAPLE PLOT

ROGERS POLYNOMIALS RE DENSITY MAPLE PLOT

Askey, Richard; Ismail, Mourad E. H., , Erdős, Paul (编), , Basel, Boston, Berlin: Birkhäuser: 55–78, 1983 [2015-01-30], ISBN 978-3-7643-1288-6, MR 0820210, （原始内容存档于2014-01-05）
Gasper, George; Rahman, Mizan, , Encyclopedia of Mathematics and its Applications 96 2nd, Cambridge University Press, 2004, ISBN 978-0-521-83357-8, MR 2128719, doi:10.2277/0521833574
Macdonald, I. G., , Cambridge Tracts in Mathematics 157, Cambridge University Press, 2003, ISBN 978-0-521-82472-9, MR 1976581, doi:10.1017/CBO9780511542824
Rogers, L. J., , Proc. London Math. Soc., 1892, 24 (1): 337–352, JFM 25.0432.01, doi:10.1112/plms/s1-24.1.337
Rogers, L. J., , Proc. London Math. Soc., 1893, 25 (1): 318–343, doi:10.1112/plms/s1-25.1.318
Rogers, L. J., , Proc. London Math. Soc., 1894, 26 (1): 15–32, doi:10.1112/plms/s1-26.1.15

Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues,p469,Springer 2010

Askey, Richard; Ismail, Mourad E. H., , Erdős, Paul (编), , Basel, Boston, Berlin: Birkhäuser: 55–78, 1983 [2015-01-30], ISBN 978-3-7643-1288-6, MR 0820210, （原始内容存档于2014-01-05）
Gasper, George; Rahman, Mizan, , Encyclopedia of Mathematics and its Applications 96 2nd, Cambridge University Press, 2004, ISBN 978-0-521-83357-8, MR 2128719, doi:10.2277/0521833574
Macdonald, I. G., , Cambridge Tracts in Mathematics 157, Cambridge University Press, 2003, ISBN 978-0-521-82472-9, MR 1976581, doi:10.1017/CBO9780511542824
Rogers, L. J., , Proc. London Math. Soc., 1892, 24 (1): 337–352, JFM 25.0432.01, doi:10.1112/plms/s1-24.1.337
Rogers, L. J., , Proc. London Math. Soc., 1893, 25 (1): 318–343, doi:10.1112/plms/s1-25.1.318
Rogers, L. J., , Proc. London Math. Soc., 1894, 26 (1): 15–32, doi:10.1112/plms/s1-26.1.15

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