Generalized Bernstein functions - Koumandos, Stamatis; Pedersen, Henrik L. (MATHEMATICA SCANDINAVICA, 2023)
A class of functions called generalized Bernstein functions is studied. The fundamental properties of this class are given and its relation to generalized Stieltjes functions via the Laplace transform is investigated. The subclass of generalized Thorin-Bernstein functions is characterized in different ways. Examples of generalized Bernstein functions include incomplete gamma functions, Lerch’s transcendent and some hypergeometric functions.