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23
Weierstrass Elliptic and Modular
Functions
Weierstrass Elliptic Functions
23.4
Graphics
23.4
Graphics
23.5
Special Lattices
Figure 23.4.8
(See
in context
.)
3D
Help
Figure 23.4.8:
℘
(
x
+
i
y
)
with
ω
1
=
K
(
k
)
,
ω
3
=
i
K
′
(
k
)
for
−
2
K
(
k
)
≤
x
≤
2
K
(
k
)
,
0
≤
y
≤
6
K
′
(
k
)
,
k
2
=
0.9
. (The scaling makes the lattice appear to be square.)
3D
Help
ⓘ
Annotations:
Symbols:
℘
(
z
)
(=
℘
(
z
|
𝕃
)
=
℘
(
z
;
g
2
,
g
3
)
): Weierstrass
℘
-function
,
K
′
(
k
)
: Legendre’s complementary complete elliptic integral of the first kind
,
K
(
k
)
: Legendre’s complete elliptic integral of the first kind
,
i
: imaginary unit
,
𝕃
: lattice
,
x
: real part of
z
,
y
: imaginary part of
z
,
ω
1
,
ω
3
,
ω
2
=
−
ω
1
−
ω
3
: lattice generators
and
k
: modulus
Permalink:
http://dlmf.nist.gov/23.4.F8.mag
Encodings:
Magnified png
,
Vizualization
,
pdf
See also:
Annotations for
§23.4
and
Ch.23