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Mediterranean Journal of Mathematics

, Volume 1, Issue 4, pp 433–439 | Cite as

Integral Representation of Some Functions Related to the Gamma Function

  • Christian BergEmail author
Original Paper

Abstract.

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

Mathematics Subject Classification (2000).

Primary 33B15 Secondary 26A48 

Keywords.

Complete monotonicity Gamma function 

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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CopenhagenCopenhagenDenmark

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