Turán inequalities for symmetric orthogonal polynomials
A method is outlined to express a Turán determinant of solutions of a three term recurrence relation as a weighted sum of squares. This method is shown to imply the positivity of Turán determinants of symmetric Pollaczek polynomials, Lommel polynomials and q-Bessel functions.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129700001X |
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| _version_ | 1832552583362772992 |
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| author | Joaquin Bustoz Mourad E. H. Ismail |
| author_facet | Joaquin Bustoz Mourad E. H. Ismail |
| author_sort | Joaquin Bustoz |
| collection | DOAJ |
| description | A method is outlined to express a Turán determinant of solutions of a three term
recurrence relation as a weighted sum of squares. This method is shown to imply the positivity of Turán determinants of symmetric Pollaczek polynomials, Lommel polynomials and q-Bessel functions. |
| format | Article |
| id | doaj-art-a1002b0e57954d878a9bc63ba3755346 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a1002b0e57954d878a9bc63ba37553462025-02-03T05:58:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-012011710.1155/S016117129700001XTurán inequalities for symmetric orthogonal polynomialsJoaquin Bustoz0Mourad E. H. Ismail1Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USADepartment of Mathematics, University of South Florida, Tampa, Florida 33620, USAA method is outlined to express a Turán determinant of solutions of a three term recurrence relation as a weighted sum of squares. This method is shown to imply the positivity of Turán determinants of symmetric Pollaczek polynomials, Lommel polynomials and q-Bessel functions.http://dx.doi.org/10.1155/S016117129700001Xrecurrence relationsTurán determinantsPollaczek polynomials Lommel polynomialsq-Bessel functions. |
| spellingShingle | Joaquin Bustoz Mourad E. H. Ismail Turán inequalities for symmetric orthogonal polynomials International Journal of Mathematics and Mathematical Sciences recurrence relations Turán determinants Pollaczek polynomials Lommel polynomials q-Bessel functions. |
| title | Turán inequalities for symmetric orthogonal polynomials |
| title_full | Turán inequalities for symmetric orthogonal polynomials |
| title_fullStr | Turán inequalities for symmetric orthogonal polynomials |
| title_full_unstemmed | Turán inequalities for symmetric orthogonal polynomials |
| title_short | Turán inequalities for symmetric orthogonal polynomials |
| title_sort | turan inequalities for symmetric orthogonal polynomials |
| topic | recurrence relations Turán determinants Pollaczek polynomials Lommel polynomials q-Bessel functions. |
| url | http://dx.doi.org/10.1155/S016117129700001X |
| work_keys_str_mv | AT joaquinbustoz turaninequalitiesforsymmetricorthogonalpolynomials AT mouradehismail turaninequalitiesforsymmetricorthogonalpolynomials |