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Statements
∂
F
(
ϕ
,
k
)
∂
k
=
E
(
ϕ
,
k
)
-
k
′
2
F
(
ϕ
,
k
)
k
k
′
2
-
k
sin
ϕ
cos
ϕ
k
′
2
1
-
k
2
sin
2
ϕ
,
partial-derivative
elliptic-integral-first-kind-F
italic-ϕ
𝑘
𝑘
elliptic-integral-second-kind-E
italic-ϕ
𝑘
superscript
superscript
𝑘
′
2
elliptic-integral-first-kind-F
italic-ϕ
𝑘
𝑘
superscript
superscript
𝑘
′
2
𝑘
italic-ϕ
italic-ϕ
superscript
superscript
𝑘
′
2
1
superscript
𝑘
2
2
italic-ϕ
{\displaystyle{\displaystyle\frac{\partial F\left(\phi,k\right)}{\partial k}={%
\frac{E\left(\phi,k\right)-{k^{\prime}}^{2}F\left(\phi,k\right)}{k{k^{\prime}}%
^{2}}-\frac{k\sin\phi\cos\phi}{{k^{\prime}}^{2}\sqrt{1-k^{2}{\sin^{2}}\phi}}},}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
F
(
ϕ
,
k
)
elliptic-integral-first-kind-F
italic-ϕ
𝑘
{\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}
E
(
ϕ
,
k
)
elliptic-integral-second-kind-E
italic-ϕ
𝑘
{\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}
∂
f
∂
x
partial-derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
∂
x
𝑥
{\displaystyle{\displaystyle\partial\NVar{x}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
ϕ
italic-ϕ
{\displaystyle{\displaystyle\phi}}
k
𝑘
{\displaystyle{\displaystyle k}}
k
′
superscript
𝑘
′
{\displaystyle{\displaystyle k^{\prime}}}
Identifiers
