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Statements
π ππΈ
2
β’
n
+
2
m
β‘
(
z
,
k
2
)
=
dn
β‘
(
z
,
k
)
β’
β
p
=
0
n
C
2
β’
p
+
1
β’
T
2
β’
p
+
1
β‘
(
sn
β‘
(
z
,
k
)
)
,
Lame-polynomial-sdE
π
2
π
2
π§
superscript
π
2
Jacobi-elliptic-dn
π§
π
superscript
subscript
π
0
π
subscript
πΆ
2
π
1
Chebyshev-polynomial-first-kind-T
2
π
1
Jacobi-elliptic-sn
π§
π
{\displaystyle{\displaystyle\mathit{sdE}^{m}_{2n+2}\left(z,k^{2}\right)=%
\operatorname{dn}\left(z,k\right)\sum_{p=0}^{n}C_{2p+1}T_{2p+1}\left(%
\operatorname{sn}\left(z,k\right)\right),}}
T
n
β‘
(
x
)
Chebyshev-polynomial-first-kind-T
π
π₯
{\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\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 ππΈ
2
β’
n
+
2
m
β‘
(
z
,
k
2
)
Lame-polynomial-sdE
π
2
π
2
π§
superscript
π
2
{\displaystyle{\displaystyle\mathit{sdE}^{\NVar{m}}_{2\NVar{n}+2}\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}}
C
2
β’
p
+
1
subscript
πΆ
2
π
1
{\displaystyle{\displaystyle C_{2p+1}}}
Identifiers
