DLMF
Menu
Index
Notations
Search
Help?
Citing
Customize
Annotate
UnAnnotate
About the Project
22
Jacobian Elliptic Functions
Properties
22.3
Graphics
22.3
Graphics
22.4
Periods, Poles, and Zeros
Figure 22.3.2
(See
in context
.)
Figure 22.3.2:
k
=
0.7
,
−
3
K
≤
x
≤
3
K
,
K
=
1.8456
…
. For
cn
(
x
,
k
)
the curve for
k
=
1
/
2
=
0.70710
…
is a boundary between the curves that have an inflection point in the interval
0
≤
x
≤
2
K
(
k
)
, and its translates, and those that do not; see
Walker (
1996
, p. 146)
.
ⓘ
Annotations:
Symbols:
cn
(
z
,
k
)
: Jacobian elliptic function
,
dn
(
z
,
k
)
: Jacobian elliptic function
,
sn
(
z
,
k
)
: Jacobian elliptic function
,
K
(
k
)
: Legendre’s complete elliptic integral of the first kind
,
x
: real
and
k
: modulus
Permalink:
http://dlmf.nist.gov/22.3.F2.mag
Encodings:
Magnified png
,
pdf
See also:
Annotations for
§22.3
and
Ch.22
