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Statements
∇
2
=
1
h
ξ
h
η
h
ϕ
(
∂
∂
ξ
(
h
η
h
ϕ
h
ξ
∂
∂
ξ
)
+
∂
∂
η
(
h
ξ
h
ϕ
h
η
∂
∂
η
)
+
∂
∂
ϕ
(
h
ξ
h
η
h
ϕ
∂
∂
ϕ
)
)
=
1
c
2
(
ξ
2
-
η
2
)
(
∂
∂
ξ
(
(
ξ
2
-
1
)
∂
∂
ξ
)
+
∂
∂
η
(
(
1
-
η
2
)
∂
∂
η
)
+
ξ
2
-
η
2
(
ξ
2
-
1
)
(
1
-
η
2
)
∂
2
∂
ϕ
2
)
.
superscript
∇
2
1
subscript
ℎ
𝜉
subscript
ℎ
𝜂
subscript
ℎ
italic-ϕ
partial-derivative
𝜉
subscript
ℎ
𝜂
subscript
ℎ
italic-ϕ
subscript
ℎ
𝜉
partial-derivative
𝜉
partial-derivative
𝜂
subscript
ℎ
𝜉
subscript
ℎ
italic-ϕ
subscript
ℎ
𝜂
partial-derivative
𝜂
partial-derivative
italic-ϕ
subscript
ℎ
𝜉
subscript
ℎ
𝜂
subscript
ℎ
italic-ϕ
partial-derivative
italic-ϕ
1
superscript
𝑐
2
superscript
𝜉
2
superscript
𝜂
2
partial-derivative
𝜉
superscript
𝜉
2
1
partial-derivative
𝜉
partial-derivative
𝜂
1
superscript
𝜂
2
partial-derivative
𝜂
superscript
𝜉
2
superscript
𝜂
2
superscript
𝜉
2
1
1
superscript
𝜂
2
partial-derivative
italic-ϕ
2
{\displaystyle{\displaystyle\nabla^{2}=\frac{1}{h_{\xi}h_{\eta}h_{\phi}}\left(%
\frac{\partial}{\partial\xi}\left(\frac{h_{\eta}h_{\phi}}{h_{\xi}}\frac{%
\partial}{\partial\xi}\right)+\frac{\partial}{\partial\eta}\left(\frac{h_{\xi}%
h_{\phi}}{h_{\eta}}\frac{\partial}{\partial\eta}\right)+\frac{\partial}{%
\partial\phi}\left(\frac{h_{\xi}h_{\eta}}{h_{\phi}}\frac{\partial}{\partial%
\phi}\right)\right)=\frac{1}{c^{2}(\xi^{2}-\eta^{2})}\left(\frac{\partial}{%
\partial\xi}\left((\xi^{2}-1)\frac{\partial}{\partial\xi}\right)+\frac{%
\partial}{\partial\eta}\left((1-\eta^{2})\frac{\partial}{\partial\eta}\right)+%
\frac{\xi^{2}-\eta^{2}}{(\xi^{2}-1)(1-\eta^{2})}\frac{{\partial}^{2}}{{%
\partial\phi}^{2}}\right).}}
∂
f
∂
x
partial-derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
∂
x
𝑥
{\displaystyle{\displaystyle\partial\NVar{x}}}
ξ
𝜉
{\displaystyle{\displaystyle\xi}}
η
𝜂
{\displaystyle{\displaystyle\eta}}
ϕ
italic-ϕ
{\displaystyle{\displaystyle\phi}}
c
𝑐
{\displaystyle{\displaystyle c}}
h
ξ
,
h
η
,
h
ϕ
subscript
ℎ
𝜉
subscript
ℎ
𝜂
subscript
ℎ
italic-ϕ
{\displaystyle{\displaystyle h_{\xi},h_{\eta},h_{\phi}}}
Identifiers
