Expansions of one density via polynomials orthogonal with respect to the other

Details Expansions of one density via polynomials orthogonal with respect to the other Expansions of one density via polynomials orthogonal with respect to the other

2010-11-05

arxiv.org/abs/1011.1492v5

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1016/j.jfa.2011.04.002

We expand the Chebyshev polynomials and some of its linear combination in linear combinations of the q-Hermite, the Rogers (q-utraspherical) and the Al-Salam--Chihara polynomials and vice versa. We use these expansions to obtain expansions of some densities, including q-Normal and some related to it, in infinite series constructed of the products of the other density times polynomials orthogonal to it, allowing deeper analysis and discovering new properties. On the way we find an easy proof of expansion of the Poisson--Mehler kernel as well as its reciprocal. We also formulate simple rule relating one set of orthogonal polynomials to the other given the properties of the ratio of the respective densities of measures orthogonalizing these polynomials sets.

Affiliated with

Also associated with

No associations

Rating

Expansions of one density via polynomials orthogonal with respect to the other 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 Expansions of one density via polynomials orthogonal with respect to the other, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Expansions of one density via polynomials orthogonal with respect to the other will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-456008