I found this asymptotic limit involving the gamma function in wikipedia. I want to find a proper reference to it (paper, book) if possible.
https://upload.wikimedia.org/math/a/f/1/af1035db85883042c71a9ab0d48d56d1.png
http://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/TranscendencePeriods.pdf
http://dlmf.nist.gov/5.11
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