By using a symmetric generalization of Sturm–Liouville problems in q-difference spaces, we introduce two finite sequences of symmetric q-orthogonal polynomials and obtain their basic properties such as a second-order q-difference equations, the explicit form of the polynomials in terms of basic hypergeometric series, three-term recurrence relations and norm-square values based on a Ramanujan identity. We also show that one of the introduced sequences is connected with the little q-Jacobi polynomials.

中文翻译：

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由两个 q-Sturm-Liouville 问题生成的对称 q-正交多项式的两个有限序列

通过在 q 差分空间中使用 Sturm-Liouville 问题的对称推广，我们引入了对称 q 正交多项式的两个有限序列，并获得了它们的基本性质，例如二阶 q 差分方程，其中多项式的显式形式基于拉马努金恒等式的基本超几何级数、三项递推关系和范数平方值。我们还表明引入的序列之一与小的 q-Jacobi 多项式有关。