论文标题
光谱特性与广义互补的Romanovski-Routh多项式有关
Spectral properties related to generalized complementary Romanovski-Routh polynomials
论文作者
论文摘要
互补的Romanovski-Routh多项式在提取正交多项式的特定特性中起重要作用。在这项工作中，互补的Romanovski-Routh多项式（GCRR）的广义形式具有高斯超几何表示，并满足了一种称为$ r_ {II} $的复发类型，称为$ r_ {II} $ type三个项复发关系，涉及两个涉及两个任意参数。确定了$ r_ {ii} $类型正交多项式的两种不同类型的GCRR多项式的自我扰动。分析了这些结果多项式的光谱特性，分析了三基因线性铅笔。这些铅笔矩阵的LU分解提供了涉及生物三相的有趣特性。讨论中多项式的零之间的隔离特性已建立。
Complementary Romanovski-Routh polynomials play an important role in extracting specific properties of orthogonal polynomials. In this work, a generalized form of the Complementary Romanovski-Routh polynomials (GCRR) that has the Gaussian hypergeometric representation and satisfies a particular type of recurrence called $R_{II}$ type three term recurrence relation involving two arbitrary parameters is considered. Self perturbation of GCRR polynomials leading to extracting two different types of $R_{II}$ type orthogonal polynomials are identified. Spectral properties of these resultant polynomials in terms of tri-diagonal linear pencil were analyzed. The LU decomposition of these pencil matrices provided interesting properties involving biorthogonality. Interlacing properties between the zeros of the polynomials in the discussion are established.
