连续q-哈恩多项式以基本超几何函数定义:[1]
并且
极限关系
连续q哈恩多项式→Q梅西纳-帕拉泽克多项式
- 阿斯基-威尔逊多项式→连续q哈恩多项式
在阿斯基-威尔逊多项式中作代换 , , , , 即得连续q哈恩多项式:
图集
CONTINUOUS q hahn ABS COMPLEX3D Maple PLOT
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CONTINUOUS q hahn IIM COMPLEX3D Maple PLOT
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CONTINUOUS q hahn RE COMPLEX3D Maple PLOT
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CONTINUOUS q hahn ABS densitu Maple PLOT
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CONTINUOUS q hahn im densitu Maple PLOT
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CONTINUOUS q hahn RE densitu Maple PLOT
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参考文献
- 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., Chapter 18: Orthogonal Polynomials, Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (编), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248
- ^ Roelof, p433