New orthogonality relations for the continuous and the discrete q-ultraspherical polynomials
Copyright policy )New orthogonality relations for the continuous and the discrete q-ultraspherical polynomials
The authors distinguish two kinds of \(q\)-ultraspherical polynomials. The first family is the well-known family of continuous \(q\)-ultraspherical polynomials introduced and studied by Rogers. In the cases where the parameters do not satisfy the conditions of Favard's theorem, the authors prove an orthogonality relation in terms of the Askey-Wilson divided difference operator \(D_q\). This is called a \(D_q\)-Sobolev orthogonality relation. The second family is a special case of the big \(q\)-Jacobi polynomials, which can be seen as a discrete \(q\)-analogue of the ultraspherical or Gegenbauer polynomials. Also in this case the authors prove a \(D_q\)-Sobolev orthogonality relation in the case that the parameters do not satisfy the conditions of Favard's theorem.
- University of Jaén Spain
non-standard orthogonality, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Applied Mathematics, Favard's theorem, discrete \(q\)-ultraspherical polynomials, Discrete q-ultraspherical polynomials, Non-standard orthogonality, Continuous q-ultraspherical polynomials, continuous \(q\)-ultraspherical polynomials, Analysis
non-standard orthogonality, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Applied Mathematics, Favard's theorem, discrete \(q\)-ultraspherical polynomials, Discrete q-ultraspherical polynomials, Non-standard orthogonality, Continuous q-ultraspherical polynomials, continuous \(q\)-ultraspherical polynomials, Analysis
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!