Completely monotonic functions related to logarithmic derivatives of entire functions

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The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)p(xml(x))(m+p) is a completely monotonic function for all m ≥ 0. This generalizes earlier results on complete monotonicity of functions related to Euler's psi-function. Applications to Barnes' multiple gamma functions are given.
TidsskriftAnalysis and Applications
Udgave nummer4
Sider (fra-til)409-419
StatusUdgivet - 2011

ID: 131444681