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Statements
d
2
w
d
ζ
2
+
(
(
2
γ
-
1
)
cn
ζ
dn
ζ
sn
ζ
-
(
2
δ
-
1
)
sn
ζ
dn
ζ
cn
ζ
-
(
2
ϵ
-
1
)
k
2
sn
ζ
cn
ζ
dn
ζ
)
d
w
d
ζ
+
4
k
2
(
α
β
sn
2
ζ
-
q
)
w
=
0
.
derivative
𝑤
𝜁
2
2
𝛾
1
Jacobi-elliptic-cn
𝜁
𝑘
Jacobi-elliptic-dn
𝜁
𝑘
Jacobi-elliptic-sn
𝜁
𝑘
2
𝛿
1
Jacobi-elliptic-sn
𝜁
𝑘
Jacobi-elliptic-dn
𝜁
𝑘
Jacobi-elliptic-cn
𝜁
𝑘
2
italic-ϵ
1
superscript
𝑘
2
Jacobi-elliptic-sn
𝜁
𝑘
Jacobi-elliptic-cn
𝜁
𝑘
Jacobi-elliptic-dn
𝜁
𝑘
derivative
𝑤
𝜁
4
superscript
𝑘
2
𝛼
𝛽
Jacobi-elliptic-sn
2
𝜁
𝑘
𝑞
𝑤
0
{\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\zeta}^{2}}+%
\left((2\gamma-1)\frac{\operatorname{cn}\zeta\operatorname{dn}\zeta}{%
\operatorname{sn}\zeta}-(2\delta-1)\frac{\operatorname{sn}\zeta\operatorname{%
dn}\zeta}{\operatorname{cn}\zeta}-(2\epsilon-1)k^{2}\frac{\operatorname{sn}%
\zeta\operatorname{cn}\zeta}{\operatorname{dn}\zeta}\right)\frac{\mathrm{d}w}{%
\mathrm{d}\zeta}+4k^{2}(\alpha\beta{\operatorname{sn}^{2}}\zeta-q)w=0.}}
cn
(
z
,
k
)
Jacobi-elliptic-cn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
dn
(
z
,
k
)
Jacobi-elliptic-dn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
sn
(
z
,
k
)
Jacobi-elliptic-sn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
d
f
d
x
derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
γ
𝛾
{\displaystyle{\displaystyle\gamma}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
ϵ
italic-ϵ
{\displaystyle{\displaystyle\epsilon}}
q
𝑞
{\displaystyle{\displaystyle q}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
β
𝛽
{\displaystyle{\displaystyle\beta}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
k
𝑘
{\displaystyle{\displaystyle k}}
Identifiers
