Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Orthogonality of a new family of $q$-Sobolev type polynomials (2312.04340v1)

Published 7 Dec 2023 in math.CA

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.

Summary

We haven't generated a summary for this paper yet.