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Spectral properties related to generalized complementary Romanovski–Routh polynomials

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

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 are 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.

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There is no external data used and the information about the results are given in the references and cited at appropriate places.

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Acknowledgements

The authors express their sincere gratitude to the anonymous referees for their constructive criticism that helped in improvement of the manuscript. The work of the second author is supported by the NBHM(DAE) Project No. NBHM/RP-1/2019.

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  1. Department of Mathematics, Indian Institute of Technology, Roorkee, Uttarakhand, 247667, India

    Vinay Shukla & A. Swaminathan

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  1. Vinay Shukla
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Shukla, V., Swaminathan, A. Spectral properties related to generalized complementary Romanovski–Routh polynomials. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 78 (2023). https://doi.org/10.1007/s13398-023-01410-0

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