The tabulation of Mathieu functions
نویسندگان
چکیده
منابع مشابه
The Tabulation of Mathieu Functions
and in which a and 6 are constants, arises in applied mathematics in two main groups of problems. The first group, of which Mathieu's problem of the transverse vibrations of a taut elliptic membrane is typical, consists of boundary problems relative to some partial differential equation, such as the wave equation, where the boundary is an ellipse—or possibly a hyperbola. Here a fundamental requ...
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For theMathieu differential equation y(x)+[a−2q cos(x)]y(x) = 0with purely imaginary parameter q = is, the characteristic value a exhibits branching points. We analyze the properties of the Mathieu functions and their Fourier coefficients in the vicinity of the branching points. Symmetry relations for the Mathieu functions as well as the Fourier coefficients behind a branching point are given. ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1945
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1945-0012907-2