Spectral properties related to generalized complementary Romanovski–Routh polynomials

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...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2023-04, Vol.117 (2), Article 78
Main Authors: Shukla, Vinay, Swaminathan, A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Perturbation
Polynomials
Theoretical
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Summary: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.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-023-01410-0