连续双哈恩多项式

连续双哈恩多项式(Continuous dual Hahn polynomials)是一个正交多项式，由下列广义超几何函数定义^[1]

S_{n} (x^{2}; a, b, c) =_{3} F_{2} (- n, a + i x, a - i x; a + b, a + c; 1) .

$\begin{matrix} R 1 & = (a + 2.3) * (a + 3.5) * h y p e r g e o m ([- 1, a + I * x, a - I * x], [a + 2.3, a + 3.5], 1) \\ R 2 & = p o c h h a m m e r (a + 2.3, 2) * p o c h h a m m e r (a + 3.5, 2) * h y p e r g e o m ([- 2, a + I * x, a - I * x], [a + 2.3, a + 3.5], 1) \\ R 3 & = p o c h h a m m e r (a + 2.3, 3) * p o c h h a m m e r (a + 3.5, 3) * h y p e r g e o m ([- 3, a + I * x, a - I * x], [a + 2.3, a + 3.5], 1) . \end{matrix}$

参考文献

↑ Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, doi:10.1007/978-3-642-05014-5, ISBN 978-3-642-05013-8, MR 2656096

Template:Q超几何函数

[1] Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, doi:10.1007/978-3-642-05014-5, ISBN 978-3-642-05013-8, MR 2656096

[1]

连续双哈恩多项式

参考文献

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