68,884 research outputs found
On the Laplace transform of absolutely monotonic functions
We obtain necessary and sufficient conditions on a function in order that it
be the Laplace transform of an absolutely monotonic function. Several closely
related results are also given.Comment: 15 page
New Upper Bounds in the Second Kershaw's Double Inequality and its Generalizations
In the paper, new upper bounds in the second Kershaw’s double
inequality and its generalizations involving the gamma, psi and polygamma
functions are established, some known results are refined
Completely monotonic ratios of basic and ordinary gamma functions
We investigate conditions for logarithmic complete monotonicity of product
ratios of gamma and q-gamma functions whose arguments are linear functions of
the variable. We give necessary and sufficient conditions in terms of
nonnegativity of a certain explicitly written measure in the q case and of a
certain elementary function in the classical q=1 case. In the latter case we
further provide simple new sufficient conditions leading to many new examples
of logarithmically completely monotonic gamma ratios. Finally, we apply some of
our results to study monotonicity of some gamma ratios and rational functions.Comment: 23 pages; no figure
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