Geodesic
A~finite expression of characteristic matrices of slightly bent elastic layers
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 11, Tome 104 (1981), pp. 156-169

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The wave propagation in the two dimension medium is investigated in the case of the cylindrical and spherical homogeneous elastic layers. For these layers the finite expressions of characteristic matrices are deduced. The comparision of these expressions and the use of Hankel function asymptotica allow to derive the formulas for slightly bent elastic layers. These finite formulas correspond to the recently obtained expressions with matrix series [1]. 
@article{ZNSL_1981_104_a15,
     author = {L. A. Molotkov},
     title = {A~finite expression of characteristic matrices of slightly bent elastic layers},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {156--169},
     publisher = {mathdoc},
     volume = {104},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a15/}
}
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L. A. Molotkov. A~finite expression of characteristic matrices of slightly bent elastic layers. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 11, Tome 104 (1981), pp. 156-169. http://geodesic.mathdoc.fr/item/ZNSL_1981_104_a15/