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28 Mathieu Functions and Hill’s EquationMathieu Functions of Noninteger Order

§28.13 Graphics


§28.13(i) Eigenvalues λν(q) for General ν

See accompanying text
Figure 28.13.1: λν(q) as a function of q for ν=0.5(1)3.5 and an(q),bn(q) for n=0,1,2,3,4 (a’s), n=1,2,3,4 (b’s). (Compare Figure 28.2.1.) Magnify
Figure 28.13.2: λν(q) for -2<ν<2, 0q10. Magnify

§28.13(ii) Solutions ceν(x,q), seν(x,q), and meν(x,q) for General ν

Figure 28.13.3: ceν(x,1) for -1<ν<1, 0x2π. Magnify
Figure 28.13.4: seν(x,1) for 0<ν<1, 0x2π. Magnify
Figure 28.13.5: meiμ(x,1) for 0.1μ0.4, -πxπ. Magnify