Geodesic
The special function ش , II
Kragujevac Journal of Mathematics, Tome 29 (2006) no. 1 
Andrea Ossicini. The special function ش , II. Kragujevac Journal of Mathematics, Tome 29 (2006) no. 1. http://geodesic.mathdoc.fr/item/KJM_2006_29_1_a13/
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     author = {Andrea Ossicini},
     title = {The special function ش , {II}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {141 - 150},
     year = {2006},
     volume = {29},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/KJM_2006_29_1_a13/}
}
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Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We describe a method for estimating the special function ^s> , in the complex cut plane $A = {\mathbf{C}}\backslash łeft( { - \infty ,0} \right]$, with a Stieltjes transform, which implies that the function ^s> is \textit{logarithmically completely monotonic}. To be complete, we find a nearly exact integral representation. At the end, we also establish that $1 \mathord{łeft/ {\vphantom {1 }} \right. \kern-\nulldelimiterspace} \mbox{^s>} łeft( x \right)$ is a complete Bernstein function and we give the representation formula which is analogous to the L\'evy-Khinchin formula.