Fundamental solutions for the Tricomi operator. II
The explicit calculation of the fundamental solutions for the Tricomi operator \({\mathfrak I}u=yu_{xx}+u_{yy}\) -- one of the simplest examples of a partial differential operator of mixed type -- is under consideration. It is shown that all such fundamental solutions originate from the hypergeometric function \(F(1/6,1/6; 1;\xi)\) that is obtained in the process of looking for homogeneous solutions to reduced hyperbolic Tricomi equation. For Part I, see ibid. 98, No. 3, 465-4-83 (1999; Zbl 0945.35063), and Correction to: ''Fundamental solutions for the Tricomi operator, II'', Duke Math. J. 117, No. 2, 385--387 (2002).
scientific article; zbMATH DE number 1820883