Through a finite-dimensional reduction of the difference Lamé equation, an elliptic analog of the Kac–Sylvester tridiagonal matrix is found. We solve the corresponding finite discrete Lamé equation by constructing an orthogonal basis of eigenvectors for this novel elliptic Kac–Sylvester matrix.

中文翻译：

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差分Lamé方程的椭圆Kac-Sylvester矩阵

通过对差分Lamé方程进行有限维简化，可以找到Kac-Sylvester三对角矩阵的椭圆类似物。我们通过为这个新颖的椭圆形Kac-Sylvester矩阵构建本征向量的正交基础，来解决相应的有限离散Lamé方程。