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22
Jacobian Elliptic Functions
Properties
22.16
Related Functions
22.16
Related Functions
22.17
Moduli Outside the Interval [0,1]
Figure 22.16.2
(See
in context
.)
Figure 22.16.2:
Jacobi’s epsilon function
ℰ
(
x
,
k
)
for
0
≤
x
≤
10
π
and
k
=
0.4
,
0.7
,
0.99
,
0.999999
. (These graphs are similar to those in Figure
22.16.1
; compare (
22.16.3
), (
22.16.17
), and the graphs of
dn
(
x
,
k
)
in §
22.3(i)
.)
ⓘ
Annotations:
Symbols:
ℰ
(
x
,
k
)
: Jacobi’s epsilon function
,
dn
(
z
,
k
)
: Jacobian elliptic function
,
π
: the ratio of the circumference of a circle to its diameter
,
x
: real
and
k
: modulus
Permalink:
http://dlmf.nist.gov/22.16.F2.mag
Encodings:
Magnified png
,
pdf
See also:
Annotations for
§22.16
and
Ch.22
