On discrete q-ultraspherical polynomials and their duals

Details On discrete q-ultraspherical polynomials and their duals On discrete q-ultraspherical polynomials and their duals

2004-03-09

arxiv.org/abs/math/0403159v1

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

We show that a confluent case of the big q-Jacobi polynomials P_n(x;a,b,c;q), which corresponds to a=b=-c, leads to a discrete orthogonality relation for imaginary values of the parameter a (outside of its commonly known domain 01, this family represents yet another q-extension of these classical polynomials, different from the continuous q-ultraspherical polynomials of Rogers. The dual family with respect to the polynomials P_n(x;a,a,-a;q) (i.e., the dual discrete q-ultraspherical polynomials) corresponds to the indeterminate moment problem, that is, these polynomials have infinitely many orthogonality relations. We find orthogonality relations for these polynomials, which have not been considered before. In particular, extremal orthogonality measures for these polynomials are derived.

Affiliated with

Also associated with

No associations

Rating

On discrete q-ultraspherical polynomials and their duals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On discrete q-ultraspherical polynomials and their duals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On discrete q-ultraspherical polynomials and their duals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-181058