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29 Lamé Functions Lamé Functions 29.3 Definitions and Basic Properties 29.5 Special Cases and Limiting Forms

§29.4 Graphics

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Permalink:: http://dlmf.nist.gov/29.4
See also:: Annotations for Ch.29

Contents

§29.4(i) Eigenvalues of Lamé’s Equation: Line Graphs
§29.4(ii) Eigenvalues of Lamé’s Equation: Surfaces
§29.4(iii) Lamé Functions: Line Graphs
§29.4(iv) Lamé Functions: Surfaces

§29.4(i) Eigenvalues of Lamé’s Equation: Line Graphs

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Keywords:: Lamé functions, eigenvalues, graphics
Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/29.4.i
See also:: Annotations for §29.4 and Ch.29

See accompanying text — Figure 29.4.1: $a^{m}_{\nu}\left(0.5\right)$ , $b^{m+1}_{\nu}\left(0.5\right)$ as functions of $\nu$ for $m=0,1,2,3$ . Magnify

See accompanying text — Figure 29.4.2: $a^{3}_{\nu}\left(0.5\right)-b^{3}_{\nu}\left(0.5\right)$ as a function of $\nu$ . Magnify

See accompanying text — Figure 29.4.2: $a^{3}_{\nu}\left(0.5\right)-b^{3}_{\nu}\left(0.5\right)$ as a function of $\nu$ . Magnify

See accompanying text — Figure 29.4.4: $a^{m}_{\nu}\left(0.1\right)$ , $b^{m+1}_{\nu}\left(0.1\right)$ as functions of $\nu$ for $m=0,1,2,3$ . Magnify

See accompanying text — Figure 29.4.4: $a^{m}_{\nu}\left(0.1\right)$ , $b^{m+1}_{\nu}\left(0.1\right)$ as functions of $\nu$ for $m=0,1,2,3$ . Magnify

See accompanying text — Figure 29.4.6: $a^{2}_{\nu}\left(0.5\right)-b^{2}_{\nu}\left(0.5\right)$ as a function of $\nu$ . Magnify

See accompanying text — Figure 29.4.6: $a^{2}_{\nu}\left(0.5\right)-b^{2}_{\nu}\left(0.5\right)$ as a function of $\nu$ . Magnify

See accompanying text — Figure 29.4.8: $a^{m}_{2.5}\left(k^{2}\right)$ , $b^{m+1}_{2.5}\left(k^{2}\right)$ as functions of $k^{2}$ for $m=0,1,2$ . Magnify

§29.4(ii) Eigenvalues of Lamé’s Equation: Surfaces

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Keywords:: Lamé functions, eigenvalues, graphics
Notes:: These surfaces were produced at NIST.
Permalink:: http://dlmf.nist.gov/29.4.ii
See also:: Annotations for §29.4 and Ch.29

See accompanying text — Figure 29.4.9: $a^{0}_{\nu}\left(k^{2}\right)$ as a function of $\nu$ and $k^{2}$ . Magnify 3D Help

See accompanying text — Figure 29.4.9: $a^{0}_{\nu}\left(k^{2}\right)$ as a function of $\nu$ and $k^{2}$ . Magnify 3D Help

See accompanying text — Figure 29.4.11: $a^{1}_{\nu}\left(k^{2}\right)$ as a function of $\nu$ and $k^{2}$ . Magnify 3D Help

See accompanying text — Figure 29.4.11: $a^{1}_{\nu}\left(k^{2}\right)$ as a function of $\nu$ and $k^{2}$ . Magnify 3D Help

§29.4(iii) Lamé Functions: Line Graphs

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Keywords:: Lamé functions, graphics
Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/29.4.iii
See also:: Annotations for §29.4 and Ch.29

See accompanying text — Figure 29.4.13: $\mathit{Ec}^{m}_{1.5}\left(x,0.5\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.85407\dotsc$ . Magnify

See accompanying text — Figure 29.4.13: $\mathit{Ec}^{m}_{1.5}\left(x,0.5\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.85407\dotsc$ . Magnify

See accompanying text — Figure 29.4.15: $\mathit{Ec}^{m}_{1.5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.4.15: $\mathit{Ec}^{m}_{1.5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.4.17: $\mathit{Ec}^{m}_{1.5}\left(x,0.9\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=2.57809\dotsc$ . Magnify

See accompanying text — Figure 29.4.17: $\mathit{Ec}^{m}_{1.5}\left(x,0.9\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=2.57809\dotsc$ . Magnify

See accompanying text — Figure 29.4.19: $\mathit{Ec}^{m}_{2.5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.4.19: $\mathit{Ec}^{m}_{2.5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.4.21: $\mathit{Ec}^{m}_{2.5}\left(x,0.5\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.85407\dotsc$ . Magnify

See accompanying text — Figure 29.4.21: $\mathit{Ec}^{m}_{2.5}\left(x,0.5\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.85407\dotsc$ . Magnify

See accompanying text — Figure 29.4.23: $\mathit{Ec}^{m}_{2.5}\left(x,0.9\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=2.57809\dotsc$ . Magnify

See accompanying text — Figure 29.4.23: $\mathit{Ec}^{m}_{2.5}\left(x,0.9\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=2.57809\dotsc$ . Magnify

§29.4(iv) Lamé Functions: Surfaces

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Keywords:: Lamé functions, graphics
Notes:: These surfaces were produced at NIST.
Permalink:: http://dlmf.nist.gov/29.4.iv
See also:: Annotations for §29.4 and Ch.29

See accompanying text — Figure 29.4.25: $\mathit{Ec}^{0}_{1.5}\left(x,k^{2}\right)$ as a function of $x$ and $k^{2}$ . Magnify 3D Help

See accompanying text — Figure 29.4.25: $\mathit{Ec}^{0}_{1.5}\left(x,k^{2}\right)$ as a function of $x$ and $k^{2}$ . Magnify 3D Help

See accompanying text — Figure 29.4.27: $\mathit{Ec}^{1}_{1.5}\left(x,k^{2}\right)$ as a function of $x$ and $k^{2}$ . Magnify 3D Help

See accompanying text — Figure 29.4.27: $\mathit{Ec}^{1}_{1.5}\left(x,k^{2}\right)$ as a function of $x$ and $k^{2}$ . Magnify 3D Help

See accompanying text — Figure 29.4.29: $\mathit{Ec}^{0}_{2.5}\left(x,k^{2}\right)$ as a function of $x$ and $k^{2}$ . Magnify 3D Help

See accompanying text — Figure 29.4.29: $\mathit{Ec}^{0}_{2.5}\left(x,k^{2}\right)$ as a function of $x$ and $k^{2}$ . Magnify 3D Help

See accompanying text — Figure 29.4.31: $\mathit{Ec}^{1}_{2.5}\left(x,k^{2}\right)$ as a function of $x$ and $k^{2}$ . Magnify 3D Help

See accompanying text — Figure 29.4.31: $\mathit{Ec}^{1}_{2.5}\left(x,k^{2}\right)$ as a function of $x$ and $k^{2}$ . Magnify 3D Help

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29.3 Definitions and Basic Properties 29.5 Special Cases and Limiting Forms