Geodesic
On the Irrationality Exponent of the Number $\ln2$
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 549-564.

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We propose another method of deriving the Marcovecchio estimate for the irrationality measure of the number $\ln2$ following, for the most part, the method of proof of the irrationality of the number $\zeta(3)$ proposed by the author in 1996. The proof uses single complex integrals, the so-called Meyer $G$-functions, and is much simpler than that of Marcovecchio.
Keywords: irrational number, Marcovecchio estimate, irrationality measure, irrationality exponent, Meyer $G$-function, saddle-point method. 
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Yu. V. Nesterenko. On the Irrationality Exponent of the Number $\ln2$. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 549-564. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a6/

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