30 Spheroidal Wave Functions Properties 30.6 Functions of Complex Argument 30.8 Expansions in Series of Ferrers Functions

§30.7 Graphics

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Permalink:: http://dlmf.nist.gov/30.7
See also:: Annotations for Ch.30

Contents

§30.7(i) Eigenvalues
§30.7(ii) Functions of the First Kind
§30.7(iii) Functions of the Second Kind
§30.7(iv) Functions of Complex Argument

§30.7(i) Eigenvalues

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Keywords:: eigenvalues, graphics, spheroidal differential equation
Notes:: Figures 30.7.1–30.7.4 were produced at NIST with the aid of Maple procedures provided by the author.
Permalink:: http://dlmf.nist.gov/30.7.i
See also:: Annotations for §30.7 and Ch.30

See accompanying text — Figure 30.7.1: Eigenvalues $\lambda^{0}_{n}\left(\gamma^{2}\right)$ , $n=0,1,2,3$ , $-10\leq\gamma^{2}\leq 10$ . Magnify

See accompanying text — Figure 30.7.2: Eigenvalues $\lambda^{1}_{n}\left(\gamma^{2}\right)$ $n=1,2,3,4$ , $-10\leq\gamma^{2}\leq 10$ . Magnify

See accompanying text — Figure 30.7.3: Eigenvalues $\lambda^{5}_{n}\left(\gamma^{2}\right)$ , $n=5,6,7,8$ , $-40\leq\gamma^{2}\leq 40$ . Magnify

See accompanying text — Figure 30.7.4: Eigenvalues $\lambda^{10}_{n}\left(\gamma^{2}\right)$ , $n=10,11,12,13$ , $-50\leq\gamma^{2}\leq 150$ . Magnify

§30.7(ii) Functions of the First Kind

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Keywords:: graphics, spheroidal wave functions
Notes:: Figures 30.7.5–30.7.10 were produced at NIST with the aid of Maple procedures provided by the author.
Permalink:: http://dlmf.nist.gov/30.7.ii
See also:: Annotations for §30.7 and Ch.30

See accompanying text — Figure 30.7.5: $\mathsf{Ps}^{0}_{n}\left(x,4\right)$ , $n=0,1,2,3$ , $-1\leq x\leq 1$ . Magnify

See accompanying text — Figure 30.7.6: $\mathsf{Ps}^{0}_{n}\left(x,-4\right)$ , $n=0,1,2,3$ , $-1\leq x\leq 1$ . Magnify

See accompanying text — Figure 30.7.7: $\mathsf{Ps}^{1}_{n}\left(x,30\right)$ , $n=1,2,3,4$ , $-1\leq x\leq 1$ . Magnify

See accompanying text — Figure 30.7.8: $\mathsf{Ps}^{1}_{n}\left(x,-30\right)$ , $n=1,2,3,4$ , $-1\leq x\leq 1$ . Magnify

See accompanying text — Figure 30.7.9: $\mathsf{Ps}^{0}_{2}\left(x,\gamma^{2}\right)$ , $-1\leq x\leq 1$ , $-50\leq\gamma^{2}\leq 50$ . Magnify 3D Help

See accompanying text — Figure 30.7.10: $\mathsf{Ps}^{1}_{3}\left(x,\gamma^{2}\right)$ , $-1\leq x\leq 1$ , $-50\leq\gamma^{2}\leq 50$ . Magnify 3D Help

§30.7(iii) Functions of the Second Kind

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Notes:: Figures 30.7.11–30.7.15 were produced at NIST with the aid of Maple procedures provided by the author.
Permalink:: http://dlmf.nist.gov/30.7.iii
See also:: Annotations for §30.7 and Ch.30

See accompanying text — Figure 30.7.11: $\mathsf{Qs}^{0}_{n}\left(x,4\right)$ , $n=0,1,2,3$ , $-1<x<1$ . Magnify

See accompanying text — Figure 30.7.12: $\mathsf{Qs}^{0}_{n}\left(x,-4\right)$ , $n=0,1,2,3$ , $-1<x<1$ . Magnify

See accompanying text — Figure 30.7.13: $\mathsf{Qs}^{1}_{n}\left(x,4\right)$ , for $n=1,2,3,4$ , $-1<x<1$ . Magnify

See accompanying text — Figure 30.7.14: $\mathsf{Qs}^{1}_{n}\left(x,-4\right)$ , $n=1,2,3,4$ , $-1<x<1$ . Magnify

See accompanying text — Figure 30.7.15: $\mathsf{Qs}^{0}_{1}\left(x,\gamma^{2}\right),-1<x<1,-10\leq\gamma^{2}\leq 10$ . Magnify 3D Help

§30.7(iv) Functions of Complex Argument

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Keywords:: graphics, spheroidal wave functions
Notes:: Figures 30.7.16–30.7.21 were produced at NIST with the aid of Maple procedures provided by the author.
Referenced by:: §30.1
Permalink:: http://dlmf.nist.gov/30.7.iv
See also:: Annotations for §30.7 and Ch.30

See accompanying text — Figure 30.7.16: $|\mathit{Ps}^{0}_{0}\left(x+\mathrm{i}y,4\right)|$ , $-2\leq x\leq 2$ , $-2\leq y\leq 2$ . Magnify 3D Help

See accompanying text — Figure 30.7.17: $|\mathit{Ps}^{0}_{0}\left(x+\mathrm{i}y,-4\right)|$ , $-2\leq x\leq 2$ , $-2\leq y\leq 2$ . Magnify 3D Help

See accompanying text — Figure 30.7.18: $|\mathit{Ps}^{1}_{1}\left(x+\mathrm{i}y,4\right)|$ , $-2\leq x\leq 2$ , $-2\leq y\leq 2$ . Magnify 3D Help

See accompanying text — Figure 30.7.19: $|\mathit{Ps}^{1}_{1}\left(x+\mathrm{i}y,-4\right)|$ , $-2\leq x\leq 2$ , $-2\leq y\leq 2$ . Magnify 3D Help

See accompanying text — Figure 30.7.20: $|\mathit{Qs}^{0}_{0}\left(x+\mathrm{i}y,4\right)|$ , $-2\leq x\leq 2$ , $-2\leq y\leq 2$ . Magnify 3D Help

See accompanying text — Figure 30.7.21: $|\mathit{Qs}^{0}_{0}\left(x+\mathrm{i}y,-4\right)|$ , $-1.8\leq x\leq 1.8$ , $-2\leq y\leq 2$ . Magnify 3D Help

30.6 Functions of Complex Argument 30.8 Expansions in Series of Ferrers Functions

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