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