Hypergeometric functions and Tricomi operators: pole in the elliptic region

• J. Barros-Neto ^[1] ; Fernando Cardoso ^[2]
  1. [1] Rutgers University

     Rutgers University

     City of New Brunswick, Estados Unidos

     
  2. [2] Universidade Federal de Pernambuco

     Universidade Federal de Pernambuco

     Brasil

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 11, Nº. 3-4, 2006, págs. 309-324
• Idioma: inglés
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• Resumen

  • In this paper we obtain fundamental solutions for a class of operators of the form 12Δx,s+αs∂∂s,α∈C∖{0}.

    These include generalizations of the classical Tricomi operator as well as the Laplace–Beltrami operator on a manifold with a suitable metric. Our results are then used to obtain explicit formulas for fundamental solutions of generalized Tricomi operators.