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Statements
πΈπ
Ξ½
2
β’
m
+
2
β‘
(
z
,
k
2
)
=
dn
β‘
(
z
,
k
)
β’
β
p
=
1
β
D
2
β’
p
β’
sin
β‘
(
2
β’
p
β’
Ο
)
,
Lame-Es
2
π
2
π
π§
superscript
π
2
Jacobi-elliptic-dn
π§
π
superscript
subscript
π
1
subscript
π·
2
π
2
π
italic-Ο
{\displaystyle{\displaystyle\mathit{Es}^{2m+2}_{\nu}\left(z,k^{2}\right)=%
\operatorname{dn}\left(z,k\right)\sum_{p=1}^{\infty}D_{2p}\sin\left(2p\phi%
\right),}}
dn
β‘
(
z
,
k
)
Jacobi-elliptic-dn
π§
π
{\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
πΈπ
Ξ½
m
β‘
(
z
,
k
2
)
Lame-Es
π
π
π§
superscript
π
2
{\displaystyle{\displaystyle\mathit{Es}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},%
\NVar{k^{2}}\right)}}
sin
β‘
z
π§
{\displaystyle{\displaystyle\sin\NVar{z}}}
m
π
{\displaystyle{\displaystyle m}}
p
π
{\displaystyle{\displaystyle p}}
z
π§
{\displaystyle{\displaystyle z}}
k
π
{\displaystyle{\displaystyle k}}
Ξ½
π
{\displaystyle{\displaystyle\nu}}
Ο
italic-Ο
{\displaystyle{\displaystyle\phi}}
D
2
β’
p
subscript
π·
2
π
{\displaystyle{\displaystyle D_{2p}}}
