Geodesic
Calculation of corrections to the Fock's asymptotic formula for the wave field in a~neighbourhood of surfaces of
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 11, Tome 104 (1981), pp. 102-110

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Corrections to Fock's asymptotic formula in a penumbra in a neighbourhood of surfaces with constant curvature are obtained. The efficiency of obtained corrections is illustrated by numerical calculations. 
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     author = {V. I. Ivanov},
     title = {Calculation of corrections to the {Fock's} asymptotic formula for the wave field in a~neighbourhood of surfaces of},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     publisher = {mathdoc},
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     year = {1981},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a9/}
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V. I. Ivanov. Calculation of corrections to the Fock's asymptotic formula for the wave field in a~neighbourhood of surfaces of. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 11, Tome 104 (1981), pp. 102-110. http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a9/