Digital Library of Mathematical Functions
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10 Bessel FunctionsBessel and Hankel Functions

§10.3 Graphics

Contents

§10.3(i) Real Order and Variable

For the modulus and phase functions Mν(x), θν(x), Nν(x), and ϕν(x) see §10.18.

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Figure 10.3.1: J0(x),Y0(x),J1(x),Y1(x),0x10. Magnify
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Figure 10.3.2: J5(x),Y5(x),M5(x),0x15. Magnify
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Figure 10.3.3: J5(x),Y5(x),N5(x),0x15. Magnify
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Figure 10.3.4: θ5(x),ϕ5(x),0x15. Magnify
Figure 10.3.5: Jν(x),0x10,0ν5. Magnify
Figure 10.3.6: Yν(x),0<x10,0ν5. Magnify
Figure 10.3.7: Jν(x),0x10,0ν5. Magnify
Figure 10.3.8: Yν(x),0.2x10,0ν5. Magnify

§10.3(ii) Real Order, Complex Variable

In the graphics shown in this subsection, height corresponds to the absolute value of the function and color to the phase. See also p. About Color Map.

Figure 10.3.9: J0(x+y),-10x10,-4y4. Magnify
Figure 10.3.10: H0(1)(x+y), -10x5,-2.8y4. Principal value. There is a cut along the negative real axis. Magnify
Figure 10.3.11: J1(x+y),-10x10,-4y4. Magnify
Figure 10.3.12: H1(1)(x+y), -10x5,-2.8y4. Principal value. There is a cut along the negative real axis. Magnify
Figure 10.3.13: J5(x+y),-10x10,-4y4. Magnify
Figure 10.3.14: H5(1)(x+y), -20x10,-4y4. Principal value. There is a cut along the negative real axis. Magnify
Figure 10.3.15: J5.5(x+y), -10x10,-4y4. Principal value. There is a cut along the negative real axis. Magnify
Figure 10.3.16: H5.5(1)(x+y), -20x10,-4y4. Principal value. There is a cut along the negative real axis. Magnify

§10.3(iii) Imaginary Order, Real Variable

For the notation see §10.24.

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Figure 10.3.17: J~1/2(x),Y~1/2(x),0.01x10. Magnify
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Figure 10.3.18: J~1(x),Y~1(x),0.01x10. Magnify
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Figure 10.3.19: J~5(x),Y~5(x),0.01x10. Magnify