The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: When delay-systems characteristics meet the zeros of Kummer functions

In this paper, which is a direct continuation and generalization of the recent works by authors [17, 35], we show validity generic multiplicity-induced-dominancy property for general class linear functional differential equations with single delay, including retarded as well neutral cases. The result based on an appropriate integral representation corresponding characteristic quasipolynomial functions involving some degenerate hypergeometric functions.