Geodesic
Asymptotics of some functions generalizing the Euler gamma-function
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 11, Tome 104 (1981), pp. 123-129

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Asymptotic behavior of two classes of functions defined by some integrals is considered. The functions $1/\Gamma(z)$ and $1/\Gamma(z+1)$ are examples of functions of this classes. The problem of investigation of this functions arises from the “connection problem” for a linear ordinary differential equations with two singular points. The theorem giving asymptotics of these functions when $|z|\to\infty$ in a certain sector is proved by making use of some lemmas and saddle point method. 
@article{ZNSL_1981_104_a11,
     author = {M. A. Kovalevsky},
     title = {Asymptotics of some functions generalizing the {Euler} gamma-function},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {123--129},
     publisher = {mathdoc},
     volume = {104},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a11/}
}
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M. A. Kovalevsky. Asymptotics of some functions generalizing the Euler gamma-function. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 11, Tome 104 (1981), pp. 123-129. http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a11/