Global Sturm inequalities for the real zeros of the solutions of the Gauss hypergeometric differential equation

  • Authors:

  • Alfredo Deaòo;Javier Segura

  • Affiliations:

  • Departamento de Matemáticas, U. Carlos III de Madrid, 28911-Leganés, Madrid, Spain;Departamento de Matemáticas, Estadística y Computación. U. de Cantabria, 39005-Santander, Spain

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2007

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Abstract

Liouville-Green transformations of the Gauss hypergeometric equation with changes of variable z(x)=@!^xt^p^-^1(1-t)^q^-^1dt 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 x"i of any of its solutions in the interval (0,1). Global bounds on the differences z(x"k"+"1)-z(x"k), 0