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<p>In this work, we introduce and construct specific <i>q</i>-polynomials that are desired from the well-established families of <i>q</i>-orthogonal polynomials, namely little <i>q</i>-Jacobi polynomials and <i>q</i>-Laguerre polynomials, respectively. Subsequently, we characterize these polynomials as <i>q</i>-Sobolev type orthogonal polynomials. We examine these newly <i>q</i>-polynomials and observe that they possess integral representations in terms of little <i>q</i>-Jacobi polynomials and <i>q</i>-Laguerre polynomials. These polynomials satisfy a third-order <i>q</i>-difference equation and display an unusual four-term recurrence relation. Special cases of these polynomials are also explored and discussed. Furthermore, we explore the behavior of these <i>q</i>-orthogonal Sobolev type polynomials as the parameters vary. We also examine their zeros and interlacing properties.</p>

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Orthogonality of a new family of q-Sobolev type polynomials

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • N. Neha,
  • A. Swaminathan

摘要

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. Subsequently, we characterize these polynomials as q-Sobolev type orthogonal polynomials. We examine these newly q-polynomials and observe that they possess integral representations in terms of little q-Jacobi polynomials and q-Laguerre polynomials. These polynomials satisfy a third-order q-difference equation and display an unusual four-term recurrence relation. Special cases of these polynomials are also explored and discussed. Furthermore, we explore the behavior of these q-orthogonal Sobolev type polynomials as the parameters vary. We also examine their zeros and interlacing properties.