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Mathematics > Classical Analysis and ODEs

arXiv:2209.03506 (math)
[Submitted on 7 Sep 2022]

Title:Spectral properties related to generalized complementary Romanovski-Routh polynomials

Authors:Vinay Shukla, A. Swaminathan
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Abstract: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.
Comments: 20 pages, 3 figures
Subjects: Classical Analysis and ODEs (math.CA)
MSC classes: 42C05, 26C10, 15A18, 33C45
Cite as: arXiv:2209.03506 [math.CA]
  (or arXiv:2209.03506v1 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2209.03506

Submission history

From: Anbhu Swaminathan [view email]
[v1] Wed, 7 Sep 2022 23:55:07 UTC (66 KB)
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