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Statements
πΈπ
Ξ½
2
β’
m
+
1
β‘
(
z
,
k
2
)
=
dn
β‘
(
z
,
k
)
β’
β
p
=
0
β
C
2
β’
p
+
1
β’
cos
β‘
(
(
2
β’
p
+
1
)
β’
Ο
)
,
Lame-Ec
2
π
1
π
π§
superscript
π
2
Jacobi-elliptic-dn
π§
π
superscript
subscript
π
0
subscript
πΆ
2
π
1
2
π
1
italic-Ο
{\displaystyle{\displaystyle\mathit{Ec}^{2m+1}_{\nu}\left(z,k^{2}\right)=%
\operatorname{dn}\left(z,k\right)\sum_{p=0}^{\infty}C_{2p+1}\cos\left((2p+1)%
\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-Ec
π
π
π§
superscript
π
2
{\displaystyle{\displaystyle\mathit{Ec}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},%
\NVar{k^{2}}\right)}}
cos
β‘
z
π§
{\displaystyle{\displaystyle\cos\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}}
C
2
β’
p
+
1
subscript
πΆ
2
π
1
{\displaystyle{\displaystyle C_{2p+1}}}
