Некоторые обобщения δ-функции Дирака

Abstract

The calculation methods of integrals containing Dirac δ-functions are generalized. The same is done for the broad class of basic functions containing discontinuities. The integral determining Eyler Г-function belongs to this type. It is shown that this integral determines different generalized Г-functions which are different from the classical one. The reasons causing this difference are analysed which are relevant for all basic results of the theory of generalized functions.