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Statements
πππΈ
2
β’
n
+
2
m
β‘
(
z
,
k
2
)
=
dn
β‘
(
z
,
k
)
β’
β
p
=
0
n
D
2
β’
p
+
1
β’
sin
β‘
(
(
2
β’
p
+
1
)
β’
Ο
)
.
Lame-polynomial-cdE
π
2
π
2
π§
superscript
π
2
Jacobi-elliptic-dn
π§
π
superscript
subscript
π
0
π
subscript
π·
2
π
1
2
π
1
italic-Ο
{\displaystyle{\displaystyle\mathit{cdE}^{m}_{2n+2}\left(z,k^{2}\right)=%
\operatorname{dn}\left(z,k\right)\sum_{p=0}^{n}D_{2p+1}\sin\left((2p+1)\phi%
\right).}}
dn
β‘
(
z
,
k
)
Jacobi-elliptic-dn
π§
π
{\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
πππΈ
2
β’
n
+
2
m
β‘
(
z
,
k
2
)
Lame-polynomial-cdE
π
2
π
2
π§
superscript
π
2
{\displaystyle{\displaystyle\mathit{cdE}^{\NVar{m}}_{2\NVar{n}+2}\left(\NVar{z%
},\NVar{k^{2}}\right)}}
sin
β‘
z
π§
{\displaystyle{\displaystyle\sin\NVar{z}}}
m
π
{\displaystyle{\displaystyle m}}
n
π
{\displaystyle{\displaystyle n}}
p
π
{\displaystyle{\displaystyle p}}
z
π§
{\displaystyle{\displaystyle z}}
k
π
{\displaystyle{\displaystyle k}}
Ο
italic-Ο
{\displaystyle{\displaystyle\phi}}
D
2
β’
p
subscript
π·
2
π
{\displaystyle{\displaystyle D_{2p}}}
