Geodesic
Uniform asymptotic expansions of solutions of the Mathieu equation and the modified Mathieu equation
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 60-91

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By the method of the model equation, uniform asymptotic expansions of the Floquet solutions of the Mathieu equation and two linearly independent solutions of the modified Mathieu equation are obtained for any real values of the separation parameter contained in these equations. 
@article{ZNSL_1976_62_a6,
     author = {N. S. Grigor'ev},
     title = {Uniform asymptotic expansions of solutions of the {Mathieu} equation and the modified {Mathieu} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--91},
     publisher = {mathdoc},
     volume = {62},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a6/}
}
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N. S. Grigor'ev. Uniform asymptotic expansions of solutions of the Mathieu equation and the modified Mathieu equation. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 60-91. http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a6/