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29 Lamé Functions Lamé Polynomials 29.12 Definitions 29.14 Orthogonality

§29.13 Graphics

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Permalink:: http://dlmf.nist.gov/29.13
See also:: Annotations for Ch.29

Contents

§29.13(i) Eigenvalues for Lamé Polynomials
§29.13(ii) Lamé Polynomials: Real Variable
§29.13(iii) Lamé Polynomials: Complex Variable

§29.13(i) Eigenvalues for Lamé Polynomials

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Keywords:: Lamé polynomials, eigenvalues, graphics
Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/29.13.i
See also:: Annotations for §29.13 and Ch.29

See accompanying text — Figure 29.13.1: $a^{m}_{2}\left(k^{2}\right)$ , $b^{m}_{2}\left(k^{2}\right)$ as functions of $k^{2}$ for $m=0,1,2$ ( $a$ ’s), $m=1,2$ ( $b$ ’s). Magnify

See accompanying text — Figure 29.13.2: $a^{m}_{1}\left(k^{2}\right)$ , $b^{m}_{1}\left(k^{2}\right)$ as functions of $k^{2}$ for $m=0,1$ ( $a$ ’s), $m=1$ ( $b$ ’s). Magnify

See accompanying text — Figure 29.13.3: $a^{m}_{3}\left(k^{2}\right)$ , $b^{m}_{3}\left(k^{2}\right)$ as functions of $k^{2}$ for $m=0,1,2,3$ ( $a$ ’s), $m=1,2,3$ ( $b$ ’s). Magnify

See accompanying text — Figure 29.13.3: $a^{m}_{3}\left(k^{2}\right)$ , $b^{m}_{3}\left(k^{2}\right)$ as functions of $k^{2}$ for $m=0,1,2,3$ ( $a$ ’s), $m=1,2,3$ ( $b$ ’s). Magnify

§29.13(ii) Lamé Polynomials: Real Variable

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Keywords:: Lamé polynomials, graphics
Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/29.13.ii
See also:: Annotations for §29.13 and Ch.29

See accompanying text — Figure 29.13.5: $\mathit{uE}^{m}_{4}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.6: $\mathit{uE}^{m}_{4}\left(x,0.9\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=2.57809\dotsc$ . Magnify

See accompanying text — Figure 29.13.7: $\mathit{sE}^{m}_{5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.7: $\mathit{sE}^{m}_{5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.9: $\mathit{cE}^{m}_{5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.9: $\mathit{cE}^{m}_{5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.11: $\mathit{dE}^{m}_{5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.11: $\mathit{dE}^{m}_{5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1,2$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.13: $\mathit{scE}^{m}_{4}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.13: $\mathit{scE}^{m}_{4}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.15: $\mathit{sdE}^{m}_{4}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.15: $\mathit{sdE}^{m}_{4}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.17: $\mathit{cdE}^{m}_{4}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.17: $\mathit{cdE}^{m}_{4}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.19: $\mathit{scdE}^{m}_{5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1$ . $K=1.61244\dotsc$ . Magnify

See accompanying text — Figure 29.13.19: $\mathit{scdE}^{m}_{5}\left(x,0.1\right)$ for $-2K\leq x\leq 2K$ , $m=0,1$ . $K=1.61244\dotsc$ . Magnify

§29.13(iii) Lamé Polynomials: Complex Variable

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Keywords:: Lamé polynomials, graphics
Notes:: These surfaces were produced at NIST.
Permalink:: http://dlmf.nist.gov/29.13.iii
See also:: Annotations for §29.13 and Ch.29

See accompanying text — Figure 29.13.21: $|\mathit{uE}^{1}_{4}\left(x+\mathrm{i}y,0.1\right)|$ for $-3K\leq x\leq 3K$ , $0\leq y\leq 2{K^{\prime}}$ . $K=1.61244\dotsc$ , ${K^{\prime}}=2.57809\dotsc$ . Magnify 3D Help

See accompanying text — Figure 29.13.22: $|\mathit{uE}^{1}_{4}\left(x+\mathrm{i}y,0.5\right)|$ for $-3K\leq x\leq 3K$ , $0\leq y\leq 2{K^{\prime}}$ . $K={K^{\prime}}=1.85407\dotsc$ . Magnify 3D Help

See accompanying text — Figure 29.13.22: $|\mathit{uE}^{1}_{4}\left(x+\mathrm{i}y,0.5\right)|$ for $-3K\leq x\leq 3K$ , $0\leq y\leq 2{K^{\prime}}$ . $K={K^{\prime}}=1.85407\dotsc$ . Magnify 3D Help

29.12 Definitions 29.14 Orthogonality

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