Deaño, Alfredo,
Segura, Javier
(2007)
*
Global Sturm inequalities for the real zeros of the solutions of the Gauss hypergeometric equation.
*
Journal of Approximation Theory,
148
(1).
pp. 92-110.
ISSN 0021-9045.
(doi:10.1016/j.jat.2007.02.005)
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Official URL https://doi.org/10.1016/j.jat.2007.02.005 |

## Abstract

Liouville–Green transformations of the Gauss hypergeometric equation with changes of variable z(x) = x tp?1(1 ? t)q?1 dt are considered. When p + q = 1, p = 0 or q = 0 these transformations, together with the application of Sturm theorems, lead to properties satisfied by all the real zeros xi of any of its solutions in the interval (0, 1). Global bounds on the differences z(xk+1) ? z(xk), 0 < xk < xk+1 < 1 being consecutive zeros, and monotonicity of these distances as a function of k can be obtained. We investigate the parameter ranges for which these two different Sturm-type properties are available. Classical results for Jacobi polynomials (Szegö’s bounds, Grosjean’s inequality) are particular cases of these more general properties. Similar properties are found for other values of p and q, particularly when |p|=|| and |q|=||, and being the usual Jacobi parameters.

Item Type: | Article |
---|---|

DOI/Identification number: | 10.1016/j.jat.2007.02.005 |

Uncontrolled keywords: | Sturm comparison theorem; Hypergeometric functions; Orthogonal polynomials |

Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics |

Depositing User: | Alfredo Deano-Cabrera |

Date Deposited: | 21 Nov 2018 10:49 UTC |

Last Modified: | 30 May 2019 08:21 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/70231 (The current URI for this page, for reference purposes) |

Deaño, Alfredo: | https://orcid.org/0000-0003-1704-247X |

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