Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle
Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle
复制标题
DOI：
10.3842/sigma.2009.033
复制
发表时间：
2008-09
影响因子：
0.9
通讯作者：
S. Tsujimoto;A. Zhedanov
中科院分区：
文献类型：
--
作者：
S. Tsujimoto;A. Zhedanov
利用椭圆Frobenius行列式的技巧，我们构造了QD-算法的新的椭圆解。这些解也可以解释为离散时间户田链的椭圆解。作为副产品，我们得到了新的显式正交和双正交多项式的椭圆超几何函数3E 2（z）。其递推系数用椭圆函数表示。在退化的情况下，我们得到的Krall-Jacobi多项式和它们的双正交类似。
Using the technique of the elliptic Frobenius determinant, we construct new elliptic solutions of theQD-algorithm. These solutions can be interpreted as elliptic solutions of the discrete-time Toda chain as well. As a by-product, we obtain new explicit orthogonal and biorthogonal polynomials in terms of the elliptic hypergeometric function 3E2(z). Their recurrence coefficients are expressed in terms of the elliptic functions. In the degenerate case we obtain the Krall-Jacobi polynomials and their biorthogonal analogs.