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

§28.3 Graphics

Contents

§28.3(i) Line Graphs: Mathieu Functions with Fixed q and Variable x

Even π-Periodic Solutions

See accompanying text
Figure 28.3.1: ce2n(x,1) for 0xπ/2, n=0,1,2,3. Magnify
See accompanying text
Figure 28.3.2: ce2n(x,10) for 0xπ/2, n=0,1,2,3. Magnify

Even π-Antiperiodic Solutions

See accompanying text
Figure 28.3.3: ce2n+1(x,1) for 0xπ/2, n=0,1,2,3. Magnify
See accompanying text
Figure 28.3.4: ce2n+1(x,10) for 0xπ/2, n=0,1,2,3. Magnify

Odd π-Antiperiodic Solutions

See accompanying text
Figure 28.3.5: se2n+1(x,1) for 0xπ/2, n=0,1,2,3. Magnify
See accompanying text
Figure 28.3.6: se2n+1(x,10) for 0xπ/2, n=0,1,2,3. Magnify

Odd π-Periodic Solutions

See accompanying text
Figure 28.3.7: se2n(x,1) for 0xπ/2, n=1,2,3,4. Magnify
See accompanying text
Figure 28.3.8: se2n(x,10) for 0xπ/2, n=1,2,3,4. Magnify

For further graphs see Jahnke et al. (1966, pp. 264–265 and 268–275).

§28.3(ii) Surfaces: Mathieu Functions with Variable x and q

Figure 28.3.9: ce0(x,q) for 0x2π, 0q10. Magnify
Figure 28.3.10: se1(x,q) for 0x2π, 0q10. Magnify
Figure 28.3.11: ce1(x,q) for 0x2π, 0q10. Magnify
Figure 28.3.12: se2(x,q) for 0x2π, 0q10. Magnify
Figure 28.3.13: ce2(x,q) for 0x2π, 0q10. Magnify