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

§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

Figure 30.7.1: Eigenvalues $\lambda^{0}_{n}\left(\gamma^{2}\right)$ ,

, $-10\leq\gamma^{2}\leq 10$ . Magnify

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Symbols:: $\lambda^{\NVar{m}}_{\NVar{n}}\left(\NVar{\gamma^{2}}\right)$ : eigenvalues of the spheroidal differential equation, $n\geq m$ : integer degree and $\gamma^{2}$ : real parameter
Referenced by:: §30.7(i)
Permalink:: http://dlmf.nist.gov/30.7.F1
Encodings:: pdf, png
See also:: Annotations for §30.7(i), §30.7 and Ch.30

Figure 30.7.2: Eigenvalues $\lambda^{1}_{n}\left(\gamma^{2}\right)$

, $-10\leq\gamma^{2}\leq 10$ . Magnify

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Symbols:: $\lambda^{\NVar{m}}_{\NVar{n}}\left(\NVar{\gamma^{2}}\right)$ : eigenvalues of the spheroidal differential equation, $n\geq m$ : integer degree and $\gamma^{2}$ : real parameter
Permalink:: http://dlmf.nist.gov/30.7.F2
Encodings:: pdf, png
See also:: Annotations for §30.7(i), §30.7 and Ch.30

Figure 30.7.3: Eigenvalues $\lambda^{5}_{n}\left(\gamma^{2}\right)$ ,

, $-40\leq\gamma^{2}\leq 40$ . Magnify

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Symbols:: $\lambda^{\NVar{m}}_{\NVar{n}}\left(\NVar{\gamma^{2}}\right)$ : eigenvalues of the spheroidal differential equation, $n\geq m$ : integer degree and $\gamma^{2}$ : real parameter
Permalink:: http://dlmf.nist.gov/30.7.F3
Encodings:: pdf, png
See also:: Annotations for §30.7(i), §30.7 and Ch.30

Figure 30.7.4: Eigenvalues $\lambda^{10}_{n}\left(\gamma^{2}\right)$ ,

, $-50\leq\gamma^{2}\leq 150$ . Magnify

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Symbols:: $\lambda^{\NVar{m}}_{\NVar{n}}\left(\NVar{\gamma^{2}}\right)$ : eigenvalues of the spheroidal differential equation, $n\geq m$ : integer degree and $\gamma^{2}$ : real parameter
Referenced by:: §30.7(i)
Permalink:: http://dlmf.nist.gov/30.7.F4
Encodings:: pdf, png
See also:: Annotations for §30.7(i), §30.7 and Ch.30

§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

Figure 30.7.5: $\mathsf{Ps}^{0}_{n}\left(x,4\right)$ ,

, $-1\leq x\leq 1$ . Magnify

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Symbols:: $\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the first kind, : real variable and $n\geq m$ : integer degree
Referenced by:: §30.7(ii)
Permalink:: http://dlmf.nist.gov/30.7.F5
Encodings:: pdf, png
See also:: Annotations for §30.7(ii), §30.7 and Ch.30

Figure 30.7.6: $\mathsf{Ps}^{0}_{n}\left(x,-4\right)$ ,

, $-1\leq x\leq 1$ . Magnify

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Symbols:: $\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the first kind, : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F6
Encodings:: pdf, png
See also:: Annotations for §30.7(ii), §30.7 and Ch.30

Figure 30.7.7: $\mathsf{Ps}^{1}_{n}\left(x,30\right)$ ,

, $-1\leq x\leq 1$ . Magnify

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Symbols:: $\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the first kind, : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F7
Encodings:: pdf, png
See also:: Annotations for §30.7(ii), §30.7 and Ch.30

Figure 30.7.8: $\mathsf{Ps}^{1}_{n}\left(x,-30\right)$ ,

, $-1\leq x\leq 1$ . Magnify

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Symbols:: $\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the first kind, : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F8
Encodings:: pdf, png
See also:: Annotations for §30.7(ii), §30.7 and Ch.30

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

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Symbols:: $\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the first kind, : real variable and $\gamma^{2}$ : real parameter
Permalink:: http://dlmf.nist.gov/30.7.F9
Encodings:: Vizualization, pdf, png
See also:: Annotations for §30.7(ii), §30.7 and Ch.30

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

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Symbols:: $\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the first kind, : real variable and $\gamma^{2}$ : real parameter
Referenced by:: §30.7(ii)
Permalink:: http://dlmf.nist.gov/30.7.F10
Encodings:: Vizualization, pdf, png
See also:: Annotations for §30.7(ii), §30.7 and Ch.30

§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

Figure 30.7.11: $\mathsf{Qs}^{0}_{n}\left(x,4\right)$ ,

. Magnify

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Symbols:: $\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the second kind, : real variable and $n\geq m$ : integer degree
Referenced by:: §30.7(iii)
Permalink:: http://dlmf.nist.gov/30.7.F11
Encodings:: pdf, png
See also:: Annotations for §30.7(iii), §30.7 and Ch.30

Figure 30.7.12: $\mathsf{Qs}^{0}_{n}\left(x,-4\right)$ ,

. Magnify

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Symbols:: $\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the second kind, : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F12
Encodings:: pdf, png
See also:: Annotations for §30.7(iii), §30.7 and Ch.30

Figure 30.7.13: $\mathsf{Qs}^{1}_{n}\left(x,4\right)$ , for

. Magnify

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Symbols:: $\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the second kind, : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F13
Encodings:: pdf, png
See also:: Annotations for §30.7(iii), §30.7 and Ch.30

Figure 30.7.14: $\mathsf{Qs}^{1}_{n}\left(x,-4\right)$ ,

. Magnify

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Symbols:: $\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the second kind, : real variable and $n\geq m$ : integer degree
Permalink:: http://dlmf.nist.gov/30.7.F14
Encodings:: pdf, png
See also:: Annotations for §30.7(iii), §30.7 and Ch.30

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

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Symbols:: $\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)$ : spheroidal wave function of the second kind, : real variable and $\gamma^{2}$ : real parameter
Referenced by:: §30.7(iii)
Permalink:: http://dlmf.nist.gov/30.7.F15
Encodings:: Vizualization, pdf, png
See also:: Annotations for §30.7(iii), §30.7 and Ch.30

§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