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Statements
πΈπ
Ξ½
2
β’
m
β‘
(
z
1
,
k
2
)
β’
w
2
β’
(
K
β‘
)
-
w
2
β’
(
-
K
β‘
)
d
w
2
β’
(
z
)
/
d
z
|
z
=
0
=
β«
-
K
β‘
K
β‘
π―
Ξ½
β‘
(
y
)
β’
πΈπ
Ξ½
2
β’
m
β‘
(
z
,
k
2
)
β’
d
z
,
Lame-Ec
2
π
π
subscript
π§
1
superscript
π
2
subscript
π€
2
complete-elliptic-integral-first-kind-K
π
subscript
π€
2
complete-elliptic-integral-first-kind-K
π
evaluated-at
derivative
subscript
π€
2
π§
π§
π§
0
superscript
subscript
complete-elliptic-integral-first-kind-K
π
complete-elliptic-integral-first-kind-K
π
shorthand-Ferrers-Legendre-P-first-kind
π
π¦
Lame-Ec
2
π
π
π§
superscript
π
2
π§
{\displaystyle{\displaystyle\mathit{Ec}^{2m}_{\nu}\left(z_{1},k^{2}\right)%
\frac{w_{2}(K)-w_{2}(-K)}{\left.\ifrac{\mathrm{d}w_{2}(z)}{\mathrm{d}z}\right|%
_{z=0}}=\int_{-K}^{K}\mathsf{P}_{\nu}\left(y\right)\mathit{Ec}^{2m}_{\nu}\left%
(z,k^{2}\right)\mathrm{d}z,}}
πΈπ
Ξ½
m
β‘
(
z
,
k
2
)
Lame-Ec
π
π
π§
superscript
π
2
{\displaystyle{\displaystyle\mathit{Ec}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},%
\NVar{k^{2}}\right)}}
K
β‘
(
k
)
complete-elliptic-integral-first-kind-K
π
{\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
d
f
d
x
derivative
π
π₯
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
d
x
π₯
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
β«
{\displaystyle{\displaystyle\int}}
π―
Ξ½
β‘
(
x
)
=
π―
Ξ½
0
β‘
(
x
)
shorthand-Ferrers-Legendre-P-first-kind
π
π₯
Ferrers-Legendre-P-first-kind
0
π
π₯
{\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=%
\mathsf{P}^{0}_{\nu}\left(x\right)}}
m
π
{\displaystyle{\displaystyle m}}
y
π¦
{\displaystyle{\displaystyle y}}
z
π§
{\displaystyle{\displaystyle z}}
k
π
{\displaystyle{\displaystyle k}}
Ξ½
π
{\displaystyle{\displaystyle\nu}}
w
β’
(
z
)
π€
π§
{\displaystyle{\displaystyle w(z)}}
Identifiers
