New inequalities from classical Sturm theorems

  • Authors:

  • Alfredo Deaòo;Amparo Gil;Javier Segura

  • Affiliations:

  • Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés (Madrid), Spain;Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Avda. de Los Castros, s/n, 39005 Santander, Spain;Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Avda. de Los Castros, s/n, 39005 Santander, Spain

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2004

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Abstract

Inequalities satisfied by the zeros of the solutions of second-order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among other properties obtained, Szego's bounds on the zeros of Jacobi polynomials P"n^(^@a^,^@b^)(cos@q) for |@a|