Integral representation of some functions related to the Gamma function

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We prove that the functions Phi(x)=[Gamma(x+1)]^{1/x}(1+1/x)^x/x and log Phi(x) are Stieltjes transforms.

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Classical Analysis and ODEs, Complex Variables, 33B15; 26A48

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http://salesiana.dossiersoluciones.com/handle/123456789/73362

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411550
 http://arxiv.org/abs/math/0411550

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arXiv