Orthogonality of a new family of q-Sobolev type polynomials

2023/12/07 by Neha, Swaminathan, A.
#33D15 #33D45 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.04340

Abstract

In this work, we introduce and construct specific q-polynomials that are desired from the well-established families of q-orthogonal polynomials, namely little q-Jacobi polynomials and q-Laguerre polynomials, respectively. We examine these newly constructed q-polynomials and observe that they possess integral representations of little q-Jacobi polynomials and q-Laguerre polynomials. These polynomials solve a third-order q-difference equation and display an unconventional four-term recurrence relation. This unique recurrence relation makes us categorize them as q-Sobolev-type orthogonal polynomials. This motivation leads to defining the general Sobolev-type orthogonality for q-polynomials. Special cases of these polynomials are also explored and discussed. Furthermore, we delve into the behavior of these q-orthogonal polynomials of Sobolev type as the parameters approach 1. We also examine their zeros and interlacing properties.

Related

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