Determinant inequalities for sieved ultraspherical polynomials
Paul Turan first observed that the Legendre polynomials satisfy the inequality Pn2(x)−Pn−1(x)Pn(x)>0, −1<x<1. Inequalities of this type have since been proved for both classical and nonclassical orthogonal polynomials. In this paper, we prove such an inequality for sieved orthogonal polynom...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201004896 |
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| author | J. Bustoz I. S. Pyung |
| author_facet | J. Bustoz I. S. Pyung |
| author_sort | J. Bustoz |
| collection | DOAJ |
| description | Paul Turan first observed that the Legendre polynomials satisfy
the inequality Pn2(x)−Pn−1(x)Pn(x)>0, −1<x<1. Inequalities of this type have since been proved for both
classical and nonclassical orthogonal polynomials. In this
paper, we prove such an inequality for sieved orthogonal
polynomials of the second kind. |
| format | Article |
| id | doaj-art-57558adbeac9413ca48dde482a52037a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-57558adbeac9413ca48dde482a52037a2025-02-03T01:22:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01251174575110.1155/S0161171201004896Determinant inequalities for sieved ultraspherical polynomialsJ. Bustoz0I. S. Pyung1Department of Mathematics, Arizona State University, Tempe 85287, AZ, USAKorean Naval Academy, Kyung-Nam, Chin-Hae 645-797, KoreaPaul Turan first observed that the Legendre polynomials satisfy the inequality Pn2(x)−Pn−1(x)Pn(x)>0, −1<x<1. Inequalities of this type have since been proved for both classical and nonclassical orthogonal polynomials. In this paper, we prove such an inequality for sieved orthogonal polynomials of the second kind.http://dx.doi.org/10.1155/S0161171201004896 |
| spellingShingle | J. Bustoz I. S. Pyung Determinant inequalities for sieved ultraspherical polynomials International Journal of Mathematics and Mathematical Sciences |
| title | Determinant inequalities for sieved ultraspherical polynomials |
| title_full | Determinant inequalities for sieved ultraspherical polynomials |
| title_fullStr | Determinant inequalities for sieved ultraspherical polynomials |
| title_full_unstemmed | Determinant inequalities for sieved ultraspherical polynomials |
| title_short | Determinant inequalities for sieved ultraspherical polynomials |
| title_sort | determinant inequalities for sieved ultraspherical polynomials |
| url | http://dx.doi.org/10.1155/S0161171201004896 |
| work_keys_str_mv | AT jbustoz determinantinequalitiesforsievedultrasphericalpolynomials AT ispyung determinantinequalitiesforsievedultrasphericalpolynomials |