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Soient T 1 et T 2 deux transformees integrales classiques dont les formules inverses coincident entre elles, satisfaisant l'equation de Parseval mixte: ∫ 0 ∞ f(x)g(x)dx=∫ 0 ∞ F 1 (y)G 2 (y)dy, ou F 1 (y)=(T 1 f)(y) et G 2 (y)=(T 2 g)(y). On propose de definir la transformation generalisee T i comme l'operateur adjoint de T 2 , et inversement

A mixed Parseval equation and the generalized Hankel transformations