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14 Legendre and Related FunctionsReal Arguments

§14.4 Graphics

Contents
  1. §14.4(i) Ferrers Functions: 2D Graphs
  2. §14.4(ii) Ferrers Functions: 3D Surfaces
  3. §14.4(iii) Associated Legendre Functions: 2D Graphs
  4. §14.4(iv) Associated Legendre Functions: 3D Surfaces

§14.4(i) Ferrers Functions: 2D Graphs

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Figure 14.4.1: 𝖯ν0(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.2: 𝖰ν0(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.3: 𝖯ν1/2(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.4: 𝖰ν1/2(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.5: 𝖯ν1(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.6: 𝖰ν1(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.7: 𝖯0μ(x), μ=0,12,1,2,4. Magnify
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Figure 14.4.8: 𝖰0μ(x), μ=0,12,1,2,4. Magnify
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Figure 14.4.9: 𝖯1/2μ(x), μ=0,12,1,2,4. Magnify
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Figure 14.4.10: 𝖰1/2μ(x), μ=0,12,1,2,4. Magnify
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Figure 14.4.11: 𝖯1μ(x), μ=0,12,1,2,4. Magnify
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Figure 14.4.12: 𝖰1μ(x), μ=0,12,1,2,4. Magnify

§14.4(ii) Ferrers Functions: 3D Surfaces

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Figure 14.4.13: 𝖯ν0(x), 0ν10,1<x<1. Magnify 3D Help
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Figure 14.4.14: 𝖰ν0(x), 0ν10,1<x<1. Magnify 3D Help
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Figure 14.4.15: 𝖯0μ(x), 0μ10,1<x<1. Magnify 3D Help
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Figure 14.4.16: 𝖰0μ(x), 0μ6.2,1<x<1. Magnify 3D Help

§14.4(iii) Associated Legendre Functions: 2D Graphs

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Figure 14.4.17: Pν0(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.18: 𝑸ν0(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.19: Pν1/2(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.20: 𝑸ν1/2(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.21: Pν1(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.22: 𝑸ν1(x), ν=0,12,1,2,4. Magnify
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Figure 14.4.23: P0μ(x), μ=0,12,1,2,4. Magnify
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Figure 14.4.24: 𝑸0μ(x), μ=0,2,4,8. Magnify
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Figure 14.4.25: P1/2μ(x), μ=0,12,1,2,4. Magnify
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Figure 14.4.26: 𝑸1/2μ(x), μ=0,2,4,8. Magnify
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Figure 14.4.27: P1μ(x), μ=0,12,1,2,4. Magnify
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Figure 14.4.28: 𝑸1μ(x), μ=0,2,4,8. Magnify

§14.4(iv) Associated Legendre Functions: 3D Surfaces

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Figure 14.4.29: Pν0(x), 0ν10, 1<x<10. Magnify 3D Help
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Figure 14.4.30: 𝑸ν0(x), 0ν10, 1<x<10. Magnify 3D Help
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Figure 14.4.31: P0μ(x), 0μ10, 1<x<10. Magnify 3D Help
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Figure 14.4.32: 𝑸0μ(x), 0μ10, 1<x<10. Magnify 3D Help