Complete monotonicity and related properties of some special functions

Koumandos, Stamatis; Lamprecht, Martin

doi:10.1090/S0025-5718-2012-02629-9

Complete monotonicity and related properties of some special functions
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Math. Comp. 82 (2013), 1097-1120 Request permission

Abstract:

We completely determine the set of $s,t>0$ for which the function $L_{s,t}(x):=x-\frac {\Gamma (x+t)}{\Gamma (x+s)} x^{s-t+1}$ is a Bernstein function, that is $L_{s,t}(x)$ is positive with completely monotonic derivative on $(0, \infty )$. The complete monotonicity of several closely related functions is also established.

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