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Statements
∂
s
∂
(
1
/
k
)
=
a
2
-
b
2
F
(
ϕ
,
k
)
=
a
2
-
b
2
R
F
(
c
-
1
,
c
-
k
2
,
c
)
,
partial-derivative
𝑠
1
𝑘
superscript
𝑎
2
superscript
𝑏
2
elliptic-integral-first-kind-F
italic-ϕ
𝑘
superscript
𝑎
2
superscript
𝑏
2
Carlson-integral-RF
𝑐
1
𝑐
superscript
𝑘
2
𝑐
{\displaystyle{\displaystyle\frac{\partial s}{\partial(1/k)}=\sqrt{a^{2}-b^{2}%
}F\left(\phi,k\right)=\sqrt{a^{2}-b^{2}}R_{F}\left(c-1,c-k^{2},c\right),}}
c
=
csc
2
ϕ
𝑐
2
italic-ϕ
{\displaystyle{\displaystyle c={\csc^{2}}\phi}}
k
2
=
(
a
2
-
b
2
)
/
(
a
2
+
λ
)
superscript
𝑘
2
superscript
𝑎
2
superscript
𝑏
2
superscript
𝑎
2
𝜆
{\displaystyle{\displaystyle k^{2}=(a^{2}-b^{2})/(a^{2}+\lambda)}}
c
=
csc
2
ϕ
𝑐
2
italic-ϕ
{\displaystyle{\displaystyle c={{\csc^{2}}}\phi}}
R
F
(
x
,
y
,
z
)
Carlson-integral-RF
𝑥
𝑦
𝑧
{\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
csc
z
𝑧
{\displaystyle{\displaystyle\csc\NVar{z}}}
F
(
ϕ
,
k
)
elliptic-integral-first-kind-F
italic-ϕ
𝑘
{\displaystyle{\displaystyle F\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}}}
ϕ
italic-ϕ
{\displaystyle{\displaystyle\phi}}
k
𝑘
{\displaystyle{\displaystyle k}}
s
𝑠
{\displaystyle{\displaystyle s}}
Identifiers
