阿拉-薩拉姆-遲哈剌多項式

阿拉-薩拉姆-遲哈剌多項式(Al-Salam-Chihara polynomials)是一個以基本超幾何函數定義的正交多項式^[1]

$Q_{n}(x;a,b;q)={\frac {(ab;q)_{n}}{a^{n}}}\;_{3}\phi _{2}\left({\begin{matrix}q^{-}n&ae^{i}\theta &ae^{-}i\theta \\ab&0\end{matrix}};q,q\right)$

極限關係

阿拉-薩拉姆-遲哈剌多項式→連續q拉蓋爾多項式

AL-SALAM-CHIHARA ABS COMPLEX 3D MAPLE PLOT

AL-SALAM-CHIHARA IM COMPLEX 3D MAPLE PLOT

AL-SALAM-CHIHARA RE COMPLEX 3D MAPLE PLOT

AL-SALAM-CHIHARA ABS DENSITY MAPLE PLOT

AL-SALAM-CHIHARA IM DENSITY MAPLE PLOT

AL-SALAM-CHIHARA RE DENSITY MAPLE PLOT

^ Roelof KoeKoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p455,Springer 2010

Al-Salam, W. A.; Chihara, Theodore Seio, Convolutions of orthonormal polynomials, SIAM Journal on Mathematical Analysis, 1976, 7 (1): 16–28, ISSN 0036-1410, MR 0399537, doi:10.1137/0507003
Gasper, George; Rahman, Mizan, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications 96 2nd, Cambridge University Press, 2004, ISBN 978-0-521-83357-8, MR 2128719, doi:10.2277/0521833574
Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F., Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, 2010, ISBN 978-3-642-05013-8, MR 2656096, doi:10.1007/978-3-642-05014-5
Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F., Al-Salam–Chihara polynomials, Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (編), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR 2723248