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Statements
∂
2
𝒦
∂
r
2
+
2
(
γ
+
δ
+
ϵ
)
-
1
r
∂
𝒦
∂
r
+
1
r
2
∂
2
𝒦
∂
θ
2
+
(
2
(
δ
+
ϵ
)
-
1
)
cot
θ
-
(
2
γ
-
1
)
tan
θ
r
2
∂
𝒦
∂
θ
+
1
r
2
sin
2
θ
∂
2
𝒦
∂
ϕ
2
+
(
2
δ
-
1
)
cot
ϕ
-
(
2
ϵ
-
1
)
tan
ϕ
r
2
sin
2
θ
∂
𝒦
∂
ϕ
=
0
.
partial-derivative
𝒦
𝑟
2
2
𝛾
𝛿
italic-ϵ
1
𝑟
partial-derivative
𝒦
𝑟
1
superscript
𝑟
2
partial-derivative
𝒦
𝜃
2
2
𝛿
italic-ϵ
1
𝜃
2
𝛾
1
𝜃
superscript
𝑟
2
partial-derivative
𝒦
𝜃
1
superscript
𝑟
2
2
𝜃
partial-derivative
𝒦
italic-ϕ
2
2
𝛿
1
italic-ϕ
2
italic-ϵ
1
italic-ϕ
superscript
𝑟
2
2
𝜃
partial-derivative
𝒦
italic-ϕ
0
{\displaystyle{\displaystyle\frac{{\partial}^{2}\mathcal{K}}{{\partial r}^{2}}%
+\frac{2(\gamma+\delta+\epsilon)-1}{r}\frac{\partial\mathcal{K}}{\partial r}+%
\frac{1}{r^{2}}\frac{{\partial}^{2}\mathcal{K}}{{\partial\theta}^{2}}+\frac{(2%
(\delta+\epsilon)-1)\cot\theta-(2\gamma-1)\tan\theta}{r^{2}}\frac{\partial%
\mathcal{K}}{\partial\theta}+\frac{1}{r^{2}{\sin^{2}}\theta}\frac{{\partial}^{%
2}\mathcal{K}}{{\partial\phi}^{2}}+\frac{(2\delta-1)\cot\phi-(2\epsilon-1)\tan%
\phi}{r^{2}{\sin^{2}}\theta}\frac{\partial\mathcal{K}}{\partial\phi}=0.}}
cot
z
𝑧
{\displaystyle{\displaystyle\cot\NVar{z}}}
∂
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}}}
tan
z
𝑧
{\displaystyle{\displaystyle\tan\NVar{z}}}
γ
𝛾
{\displaystyle{\displaystyle\gamma}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
ϵ
italic-ϵ
{\displaystyle{\displaystyle\epsilon}}
𝒦
(
z
;
s
,
t
)
𝒦
𝑧
𝑠
𝑡
{\displaystyle{\displaystyle\mathcal{K}(z;s,t)}}
r
𝑟
{\displaystyle{\displaystyle r}}
θ
𝜃
{\displaystyle{\displaystyle\theta}}
ϕ
italic-ϕ
{\displaystyle{\displaystyle\phi}}
