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A class of logarithmically completely monotonic functions associated with a gamma function. (English) Zbl 1210.33004

The authors study the log complete monotonicity of the functions j\(G(x)= [e^x\Gamma(x+ a)]/(x+ b)^{x+ b}\), and \(1/G(x)\), where \(x> 0\). The proofs are based among others on integral representations, as well as inequalities for the digamma function.

MSC:

33B15 Gamma, beta and polygamma functions
26A48 Monotonic functions, generalizations
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References:

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