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22
Jacobian Elliptic Functions
Properties
22.3
Graphics
22.3
Graphics
22.4
Periods, Poles, and Zeros
Figure 22.3.24
(See
in context
.)
3D
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Figure 22.3.24:
sn
(
x
+
i
y
,
k
)
for
−
4
≤
x
≤
4
,
0
≤
y
≤
8
,
k
=
1
+
1
2
i
.
K
=
1.5149
…
+
i
0.5235
…
,
K
′
=
1.4620
…
−
i
0.3552
…
.
3D
Help
ⓘ
Annotations:
Symbols:
sn
(
z
,
k
)
: Jacobian elliptic 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
,
x
: real
,
y
: real
and
k
: modulus
Keywords:
Jacobian elliptic functions
,
complex
,
modulus
Permalink:
http://dlmf.nist.gov/22.3.F24.mag
Encodings:
Magnified png
,
Vizualization
,
pdf
See also:
Annotations for
§22.3
and
Ch.22