Geodesic
Elementary Remarks on Multiply Monotonic Functions and Sequences(1)
Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 69-72

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A function f(x) is said to be completely monotonic on (0, ∞) if 1 Familiar examples of such functions are given by f(x) = exp(—αx) and f(x) = (x+β)-α, where α ≥ 0, β ≥ 0. A discussion of completely monotonic functions is given in [5, Ch. IV]. 
Muldoon, M. E. Elementary Remarks on Multiply Monotonic Functions and Sequences(1). Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 69-72. doi: 10.4153/CMB-1971-013-5
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[1] 1. Dubourdieu, J., Sur un théorème de M. S. Bernstein relatif á la transformation de Laplace- Stieltjes, Compositio Math. 7 (1939-1940), 96-111. Google Scholar

[2] 2. Lorch, Lee and Moser, Leo, A remark on completely monotonie sequences with an application to summability, Canad. Math. Bull. 6 (1963), 171-173. Google Scholar

[3] 3. Lorch, Lee and Szego, Peter, Higher monotonicity properties of certain Sturm-Liouville functions, Acta Math. 109 (1963), 55-73. Google Scholar

[4] 4. Schoenberg, I. J., On integral representations of completely monotone and related functions (abstract), Bull. Amer. Math. Soc. 47 (1941), p. 208. Google Scholar

[5] 5. Widder, D. V., The Laplace transform, Princeton Univ. Press, Princeton, N.J., 1941. Google Scholar

[6] 6. Williamson, R. E., Multiply monotone functions and their Laplace transforms, Duke Math. J. 23 (1956), 189-207. Google Scholar

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