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Statements
nc
(
u
+
v
)
=
nc
u
nc
v
+
sc
u
dc
u
sc
v
dc
v
1
-
k
′
2
sc
2
u
sc
2
v
,
Jacobi-elliptic-nc
𝑢
𝑣
𝑘
Jacobi-elliptic-nc
𝑢
𝑘
Jacobi-elliptic-nc
𝑣
𝑘
Jacobi-elliptic-sc
𝑢
𝑘
Jacobi-elliptic-dc
𝑢
𝑘
Jacobi-elliptic-sc
𝑣
𝑘
Jacobi-elliptic-dc
𝑣
𝑘
1
superscript
superscript
𝑘
′
2
Jacobi-elliptic-sc
2
𝑢
𝑘
Jacobi-elliptic-sc
2
𝑣
𝑘
{\displaystyle{\displaystyle\operatorname{nc}(u+v)=\frac{\operatorname{nc}u%
\operatorname{nc}v+\operatorname{sc}u\operatorname{dc}u\operatorname{sc}v%
\operatorname{dc}v}{1-{k^{\prime}}^{2}{\operatorname{sc}^{2}}u{\operatorname{%
sc}^{2}}v},}}
dc
(
z
,
k
)
Jacobi-elliptic-dc
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
nc
(
z
,
k
)
Jacobi-elliptic-nc
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
sc
(
z
,
k
)
Jacobi-elliptic-sc
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
u
𝑢
{\displaystyle{\displaystyle u}}
v
𝑣
{\displaystyle{\displaystyle v}}
k
𝑘
{\displaystyle{\displaystyle k}}
