论文标题
双参数$ su（1,1）$ HEUN等式和准聚合解决方案的结构
Bi-parametric $su(1,1)$ structure of the Heun class of equations and quasi-polynomial solutions
论文作者
论文摘要
探索了HEUN方程类别的新型Bi-parametric $ su（1,1）$代数化。这产生了$ \ {z^αp_n（z）的形式的其他准多元解：\α\ in \ mathbb {c}，\ n \ in \ mathbb {n} _0 _0 \ \} $ in \ mathbb {n} _0 \ \} $ to to General Heun Eqaution及其相互交流的版本。为单个方程式提供了导致这些准多项式的明确条件，以直接使用。对于汇合和双重引起的HEUN方程，已经确定了该方程式的无限数量的准多项式和（ii），该方程式的特定参数情况已确定。
A new bi-parametric $su(1,1)$ algebraization of the Heun class of equations is explored. This yields additional quasi-polynomial solutions of the form $\{z^αP_N(z): \ α\in \mathbb{C}, \ N \in \mathbb{N}_0\}$ to the General Heun eqaution and its confluent versions. Explicit conditions leading to these quasi-polynomials have been provided for the individual equations to allow direct use. For the Confluent and the Doubly-confluent Heun equations, specific parametric situations leading to (i) an infinite number of quasi-polynomials and (ii) non-algebraizability of the equation have been identified.
