DLMF: Figure 29.13.23 ‣ §29.13 Graphics ‣ Lamé Polynomials ‣ Chapter 29 Lamé Functions

29 Lamé Functions Lamé Polynomials 29.13 Graphics 29.13 Graphics 29.14 Orthogonality

Figure 29.13.23 (See in context.)

Figure 29.13.23:

|\mathit{uE}^{1}_{4}\left(x+\mathrm{i}y,0.9\right)|

for

-3K\leq x\leq 3K

,

0\leq y\leq 2{K^{\prime}}

.

K=2.57809\dotsc

,

{K^{\prime}}=1.61244\dotsc

.

ⓘ

Annotations:

Symbols:: $\mathit{uE}^{\NVar{m}}_{2\NVar{n}}\left(\NVar{z},\NVar{k^{2}}\right)$ : Lamé polynomial, ${K^{\prime}}\left(\NVar{k}\right)$ : Legendre’s complementary complete elliptic integral of the first kind, $K\left(\NVar{k}\right)$ : Legendre’s complete elliptic integral of the first kind, $\mathrm{i}$ : imaginary unit, $x$ : real variable, $y$ : real variable and $k$ : real parameter
Permalink:: http://dlmf.nist.gov/29.13.F23.viz

29.13 Graphics 29.14 Orthogonality

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