View More View Less
  • 1 Institut Supérieur de Gestion de Gab?s, Département des Méthodes Quantitatives Rue Jilani Habib 6002-Gab?s, Tunisia Rue Jilani Habib 6002-Gab?s, Tunisia
  • 2 Faculté des Sciences de Gab?s Route de Mednine, 6029- Gab?s, Tunisia Route de Mednine, 6029- Gab?s, Tunisia
Restricted access

Summary  

A form (linear functional) \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $u$ \end{document} is called regular if we can associate with it a sequence of monic orthogonal polynomials. On certain regularity conditions, the product of a non regular form by a polynomial can be regular. The purpose of this work is to establish regularity conditions of the form $-(x-c){\mathbf S}',$ where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} ${\mathbf S}$ \end{document} is a classical (Bessel, Jacobi). We give the second-order recurrence relations and structure relations of its corresponding orthogonal polynomial sequence. We conclude with an example as an illustration.