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Statements
π πππΈ
2
β’
n
+
3
m
β‘
(
z
,
k
2
)
=
cn
β‘
(
z
,
k
)
β’
dn
β‘
(
z
,
k
)
β’
β
p
=
0
n
D
2
β’
p
+
2
β’
U
2
β’
p
+
1
β‘
(
sn
β‘
(
z
,
k
)
)
.
Lame-polynomial-scdE
π
2
π
3
π§
superscript
π
2
Jacobi-elliptic-cn
π§
π
Jacobi-elliptic-dn
π§
π
superscript
subscript
π
0
π
subscript
π·
2
π
2
Chebyshev-polynomial-second-kind-U
2
π
1
Jacobi-elliptic-sn
π§
π
{\displaystyle{\displaystyle\mathit{scdE}^{m}_{2n+3}\left(z,k^{2}\right)=%
\operatorname{cn}\left(z,k\right)\operatorname{dn}\left(z,k\right)\sum_{p=0}^{%
n}D_{2p+2}U_{2p+1}\left(\operatorname{sn}\left(z,k\right)\right).}}
U
n
β‘
(
x
)
Chebyshev-polynomial-second-kind-U
π
π₯
{\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}
cn
β‘
(
z
,
k
)
Jacobi-elliptic-cn
π§
π
{\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
dn
β‘
(
z
,
k
)
Jacobi-elliptic-dn
π§
π
{\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
sn
β‘
(
z
,
k
)
Jacobi-elliptic-sn
π§
π
{\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
π πππΈ
2
β’
n
+
3
m
β‘
(
z
,
k
2
)
Lame-polynomial-scdE
π
2
π
3
π§
superscript
π
2
{\displaystyle{\displaystyle\mathit{scdE}^{\NVar{m}}_{2\NVar{n}+3}\left(\NVar{%
z},\NVar{k^{2}}\right)}}
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}}
D
2
β’
p
+
1
subscript
π·
2
π
1
{\displaystyle{\displaystyle D_{2p+1}}}
Identifiers
