Comparative asymptotics for discrete semiclassical orthogonal polynomials
We study the ratio [Formula: see text] asymptotically as [Formula: see text], where the polynomials [Formula: see text] are orthogonal with respect to a discrete linear functional and [Formula: see text] denote the falling factorial polynomials. We give recurrences that allow the computation of high...
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2023-04-01
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| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360722500102 |
| _version_ | 1797837969642487808 |
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| author | Diego Dominici |
| author_facet | Diego Dominici |
| author_sort | Diego Dominici |
| collection | DOAJ |
| description | We study the ratio [Formula: see text] asymptotically as [Formula: see text], where the polynomials [Formula: see text] are orthogonal with respect to a discrete linear functional and [Formula: see text] denote the falling factorial polynomials. We give recurrences that allow the computation of high order asymptotic expansions of [Formula: see text] and give examples for most discrete semiclassical polynomials of class [Formula: see text]. We show several plots illustrating the accuracy of our results. |
| first_indexed | 2024-04-09T15:33:15Z |
| format | Article |
| id | doaj.art-5caba301660a40de86c3b322b962ce5b |
| institution | Directory Open Access Journal |
| issn | 1664-3607 1664-3615 |
| language | English |
| last_indexed | 2024-04-09T15:33:15Z |
| publishDate | 2023-04-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Bulletin of Mathematical Sciences |
| spelling | doaj.art-5caba301660a40de86c3b322b962ce5b2023-04-28T04:34:54ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152023-04-01130110.1142/S1664360722500102Comparative asymptotics for discrete semiclassical orthogonal polynomialsDiego Dominici0Research Institute for Symbolic Computation, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, AustriaWe study the ratio [Formula: see text] asymptotically as [Formula: see text], where the polynomials [Formula: see text] are orthogonal with respect to a discrete linear functional and [Formula: see text] denote the falling factorial polynomials. We give recurrences that allow the computation of high order asymptotic expansions of [Formula: see text] and give examples for most discrete semiclassical polynomials of class [Formula: see text]. We show several plots illustrating the accuracy of our results.https://www.worldscientific.com/doi/10.1142/S1664360722500102Semiclassical orthogonal polynomialsasymptotic expansionsordinary differential equations |
| spellingShingle | Diego Dominici Comparative asymptotics for discrete semiclassical orthogonal polynomials Bulletin of Mathematical Sciences Semiclassical orthogonal polynomials asymptotic expansions ordinary differential equations |
| title | Comparative asymptotics for discrete semiclassical orthogonal polynomials |
| title_full | Comparative asymptotics for discrete semiclassical orthogonal polynomials |
| title_fullStr | Comparative asymptotics for discrete semiclassical orthogonal polynomials |
| title_full_unstemmed | Comparative asymptotics for discrete semiclassical orthogonal polynomials |
| title_short | Comparative asymptotics for discrete semiclassical orthogonal polynomials |
| title_sort | comparative asymptotics for discrete semiclassical orthogonal polynomials |
| topic | Semiclassical orthogonal polynomials asymptotic expansions ordinary differential equations |
| url | https://www.worldscientific.com/doi/10.1142/S1664360722500102 |
| work_keys_str_mv | AT diegodominici comparativeasymptoticsfordiscretesemiclassicalorthogonalpolynomials |