Numeric-analytical construction of Mathieu functions
نویسندگان
چکیده
منابع مشابه
Hierarchical Construction of Finite Diabatic Sets, By Mathieu Functions
An extension is given for the standard two component model of adiabatic, Born-Oppenheimer (BO) electronic states in a polyatonic molecule, by use of Mathieu functions of arbitrary order. The curl or compatibility conditions for the construction of a diabatic set of states based on a finitedimensional subset of BO states are not satisfied exactly. It is shown, however, that, by successively addi...
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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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Continued fraction expansions for the eigenvalues A= A(I', h2 ) and for the Fourier coefficients c~n/co are given by Tamir and Wang in [2]. These relations are valid both in the s table (I' real) and unstable (I' complex) regions . F (I') == C~,.1Co is numerically evaluated and depicted. It is seen from the graphs in [2] that the given formulas for C~,JCO are not particularly suitable for numer...
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environments: Since the abstract counterpart for addresses are symbolic variables (or nodes) in shape graphs, an abstract environment E can simply be a function mapping program variables to nodes, that is, E ∈ E =X→V. Now, the memory abstract domainM is defined byM = E× (H ⇒ N ), and its concretization γM :M ♯ → P(E×H) can be defined as follows: γM(E ,(σ ,ν)) def = {(ν ◦E,σ) | (σ ,ν) ∈ γH(σ ) a...
متن کاملMathieu functions for purely imaginary parameters
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: Mathematica Bohemica
سال: 1999
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.1999.125982