Geodesic
Numeric-analytical construction of Mathieu functions
Mathematica Bohemica, Tome 124 (1999) no. 1, pp. 15-28

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MR Zbl
In this paper we present an iterative algorithm for the construction of Mathieu functions of any order $N$ in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.
In this paper we present an iterative algorithm for the construction of Mathieu functions of any order $N$ in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.
DOI : 10.21136/MB.1999.125982
Classification : 33E10, 34A25, 34A50, 65D15, 65D20
Keywords: Mathieu functions; iterative algorithm; Quick-BASIC program; Fourier series 
Ryabov, Yu. A. Numeric-analytical construction of Mathieu functions. Mathematica Bohemica, Tome 124 (1999) no. 1, pp. 15-28. doi: 10.21136/MB.1999.125982
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[1] Ch. Hayashi: Nonlinear Oscillations in Physical Systems. McGraw-Hill, New York, 1964. | MR | Zbl

[2] Yu. A. Ryabov: The estimations of convergence radius for series in power of parameter and algorithms for construction of Mathieu functions. Differencialnye uravnenija 15 (1979), no. 11, 1993-2003. (In Russian.) | MR

[3] B. A. Grebenikov, Yu. A. Ryabov: Constructive methods in the analysis of nonlinear systems. Mir Publishers, Moscow, 1983, translated from Russian. | MR | Zbl

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