阿拉-萨拉姆-迟哈剌多项式...
基本超几何函数Q阶乘幂Q导数Q指数Q正弦函数QΓ函数QBeta函数Q余弦函数Q阿佩尔函数
正交多项式Q-模拟特殊超几何函数
基本超几何函数正交多项式连续q拉盖尔多项式阿拉-萨拉姆-迟哈剌多项式连续大Q埃尔米特多项式
AL-SALAM-CHIHARA 2D MAPLE PLOT
阿拉-萨拉姆-迟哈剌多项式(Al-Salam-Chihara polynomials)是一个以基本超几何函数定义的正交多项式[1]
Qn(x;a,b;q)=(ab;q)nan3ϕ2(q−naeiθae−iθab0;q,q){displaystyle Q_{n}(x;a,b;q)={frac {(ab;q)_{n}}{a^{n}}};_{3}phi _{2}left({begin{matrix}q^{-}n&ae^{i}theta &ae^{-}itheta \ab&0end{matrix}};q,qright)}
极限关系
阿拉-萨拉姆-迟哈剌多项式→连续q拉盖尔多项式
令阿拉-萨拉姆-迟哈剌多项式 b=0,即得连续大Q埃尔米特多项式
图集
 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 |
参考文献
^ 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, (编) Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W., NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248
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