From continuous to discrete : weak limit of normalized Askey–Wilson measure
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
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Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 227-252 |
| Journal / Publication | Ramanujan Journal |
| Volume | 64 |
| Issue number | 1 |
| Online published | 18 Jan 2024 |
| Publication status | Published - May 2024 |
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| DOI | DOI |
|---|---|
| Attachment(s) | Documents
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| Link to Scopus | https://www.scopus.com/record/display.uri?eid=2-s2.0-85182694393&origin=recordpage |
| Permanent Link | https://scholars.cityu.edu.hk/en/publications/publication(27e33968-0459-4b78-af54-eca8dbb6f716).html |
Abstract
In this paper, we consider the weak limit of the normalized measure for Askey–Wilson polynomials when the parameter q approaches -1 from the right. We use two different methods to prove that the weak limit is a discrete measure with two mass points that are symmetric about the origin. The weights on these two mass points are, however, not always the same. We also calculate the weak limit of the q-ultraspherical measure when q approaches a complex root of unity. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
Research Area(s)
- Askey–Wilson polynomials, Orthogonality measures, Weak limit
Citation Format(s)
From continuous to discrete: weak limit of normalized Askey–Wilson measure. / Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng.
In: Ramanujan Journal, Vol. 64, No. 1, 05.2024, p. 227-252.
In: Ramanujan Journal, Vol. 64, No. 1, 05.2024, p. 227-252.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
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