Q梅西纳-帕拉泽克多项式

Q梅西纳-帕拉泽克多项式定义如下：^[1]

$P_{n} (x; a | q) = a^{- n} e^{i n ϕ}$ $\frac{a^{2}; q_{n}}{(q; q)_{n}}$ $_{3} Φ_{2} (q^{-} n, a e^{i (θ + 2 ϕ)}, a e^{- i θ}; a^{2}, 0 | q; q)$

极限关系

连续q哈恩多项式→Q梅西纳-帕拉泽克多项式

$\frac{p_{n} (c o s (θ + ϕ); a, 0, 0, a; q)}{(q; q)_{n}} = P_{n} (c o s (θ + ϕ); a | q)$

Q梅西纳-帕拉泽克多项式→连续q超球面多项式

$P_{n} (c o s ϕ; β | q) = C_{n} (c o s ϕ); β | q)$

Q梅西纳-帕拉泽克多项式→连续q拉盖尔多项式

$P_{n} (c o s (θ + ϕ); q^{α / 2 + 1 / 2} | q) =$ $q^{(- α / 2 - 1 / 4) * n} * P_{n}^{(} α) (c o s θ | q)$

↑ Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analoques, p460,Springer