Completely monotone function; Absolutely monotone function; Real analyticity; Newton series expansion; Principal indefinite sum; Higher-order convexity
Abstract :
[en] We prove that every completely monotone function defined on a right-unbounded open interval admits a Newton series expansion at every point of that interval. This result can be viewed as an analog of Bernstein's little theorem for absolutely monotone functions. As an application, we use it to study principal indefinite sums, which are constructed via a broad generalization of Bohr-Mollerup's theorem.
Disciplines :
Mathematics
Author, co-author :
LAMBY, Thomas ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
MARICHAL, Jean-Luc ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Zenaïdi, Naïm; University of Liège, Department of Mathematics, Liège, Belgium
Language :
English
Title :
Newton series representation of completely monotone functions
