Digital Library of Mathematical Functions
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30 Spheroidal Wave FunctionsProperties

§30.7 Graphics

Contents

§30.7(i) Eigenvalues

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Figure 30.7.1: Eigenvalues λn0(γ2), n=0,1,2,3, -10γ210. Magnify
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Figure 30.7.2: Eigenvalues λn1(γ2)n=1,2,3,4, -10γ210. Magnify
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Figure 30.7.3: Eigenvalues λn5(γ2), n=5,6,7,8, -40γ240. Magnify
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Figure 30.7.4: Eigenvalues λn10(γ2), n=10,11,12,13, -50γ2150. Magnify

§30.7(ii) Functions of the First Kind

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Figure 30.7.5: Psn0(x,4), n=0,1,2,3, -1x1. Magnify
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Figure 30.7.6: Psn0(x,-4), n=0,1,2,3, -1x1. Magnify
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Figure 30.7.7: Psn1(x,30), n=1,2,3,4, -1x1. Magnify
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Figure 30.7.8: Psn1(x,-30), n=1,2,3,4, -1x1. Magnify
Figure 30.7.9: Ps20(x,γ2), -1x1, -50γ250. Magnify
Figure 30.7.10: Ps31(x,γ2), -1x1, -50γ250. Magnify

§30.7(iii) Functions of the Second Kind

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Figure 30.7.11: Qsn0(x,4), n=0,1,2,3, -1<x<1. Magnify
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Figure 30.7.12: Qsn0(x,-4), n=0,1,2,3, -1<x<1. Magnify
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Figure 30.7.13: Qsn1(x,4), for n=1,2,3,4, -1<x<1. Magnify
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Figure 30.7.14: Qsn1(x,-4), n=1,2,3,4, -1<x<1. Magnify
Figure 30.7.15: Qs10(x,γ2),-1<x<1,-10γ210. Magnify

§30.7(iv) Functions of Complex Argument

Figure 30.7.16: |Ps00(x+y,4)|, -2x2, -2y2. Magnify
Figure 30.7.17: |Ps00(x+y,-4)|, -2x2, -2y2. Magnify
Figure 30.7.18: |Ps11(x+y,4)|, -2x2, -2y2. Magnify
Figure 30.7.19: |Ps11(x+y,-4)|, -2x2, -2y2. Magnify
Figure 30.7.20: |Qs00(x+y,4)|, -2x2, -2y2. Magnify
Figure 30.7.21: |Qs00(x+y,-4)|, -1.8x1.8, -2y2. Magnify