Completely Monotonic Functions in Hankel and Toeplitz Determinants

摘要

We discuss certain families of combinations of f, f(prime), f(double prime), ...,where f is a completely monotonic function on (0, infinity). We prove that these combinations are non-negative, and conjecture that they will turn out to be again completely monotonic. These combinations may be useful, for example, in the study of real powers of completely monotonic functions. (Copyright (c) 1993 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)