連續哈恩多項式

Continuous Hahn Polynomials

Continuous Hahn Polynomials

連續哈恩多項式由下列超幾何函數定義：

$p_{n}(x;a,b,c,d)=i^{n}{\frac {(a+c)_{n}(a+d)_{n}}{n!}}{}_{3}F_{2}(-n,n+a+b+c+d-1,a+ix;a+c,a+d;1)$

參考文獻

• Hahn, Wolfgang, Über Orthogonalpolynome, die q-Differenzengleichungen genügen, Mathematische Nachrichten, 1949, 2: 4–34, ISSN 0025-584X, MR 0030647, doi:10.1002/mana.19490020103 
• 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., Hahn Class: Definitions, 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, MR2723248