Abstract
The concept of absolutely monotone functions is generalized by replacing the conditionsφ (k)(t)≧0,k=0, 1, … by an infinite sequence of differential inequalitiesφ(t)≧0,L kφ(t)≧0,k=1, 2, …, where theL k are differential operators of a special type. It is shown that these functions have a valid series expansion in terms of basic functions associated with the operatorsL k.
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Karlin, S., Ziegler, Z. Generalized absolutely monotone functions. Israel J. Math. 3, 173–180 (1965). https://doi.org/10.1007/BF02759750
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DOI: https://doi.org/10.1007/BF02759750