On summable, positive Poisson-Mehler kernels built of Al-Salam--Chihara and related polynomials

Details On summable, positive Poisson-Mehler kernels built of Al-Salam--Chihara and related polynomials On summable, positive Poisson-Mehler kernels built of Al-Salam--Chihara and related polynomials

2010-11-08

arxiv.org/abs/1011.1848v4

Mathematics

Classical Analysis and ODEs

Scientific paper

Using special technique of expanding ratio of densities in an infinite series of polynomials orthogonal with respect to one of the densities, we obtain simple, closed forms of certain kernels built of the so called Al-Salam---Chihara (ASC) polynomials. We consider also kernels built of some other families of polynomials such as the so called big continuous q-Hermite polynomials that are related to the ASC polynomials. The constructed kernels are symmetric and asymmetric. Being the ratios of the densities they are automatically positive. We expand also reciprocals of some of the kernels, getting nice identities built of the ASC polynomials involving 6 variables like e.g. formula. These expansions lead to asymmetric, positive and summable kernels. The particular cases (referring to q=1 and q=0) lead to the kernels build of certain linear combinations of the ordinary Hermite and Chebyshev polynomials.

Affiliated with

Also associated with

No associations

Rating

On summable, positive Poisson-Mehler kernels built of Al-Salam--Chihara and related polynomials 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 summable, positive Poisson-Mehler kernels built of Al-Salam--Chihara and related polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On summable, positive Poisson-Mehler kernels built of Al-Salam--Chihara and related polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-131694