Deprecated : $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372 DLMF:10.73.E4 - MaRDI portal
Statements
(
∇
2
+
k
2
)
f
=
1
ρ
2
∂
∂
ρ
(
ρ
2
∂
f
∂
ρ
)
+
1
ρ
2
sin
θ
∂
∂
θ
(
sin
θ
∂
f
∂
θ
)
+
1
ρ
2
sin
2
θ
∂
2
f
∂
ϕ
2
+
k
2
f
.
superscript
∇
2
superscript
𝑘
2
𝑓
1
superscript
𝜌
2
partial-derivative
𝜌
superscript
𝜌
2
partial-derivative
𝑓
𝜌
1
superscript
𝜌
2
𝜃
partial-derivative
𝜃
𝜃
partial-derivative
𝑓
𝜃
1
superscript
𝜌
2
2
𝜃
partial-derivative
𝑓
italic-ϕ
2
superscript
𝑘
2
𝑓
{\displaystyle{\displaystyle(\nabla^{2}+k^{2})f=\frac{1}{\rho^{2}}\frac{%
\partial}{\partial\rho}\left(\rho^{2}\frac{\partial f}{\partial\rho}\right)+%
\frac{1}{\rho^{2}\sin\theta}\frac{\partial}{\partial\theta}\left(\sin\theta%
\frac{\partial f}{\partial\theta}\right)+\frac{1}{\rho^{2}{\sin^{2}}\theta}%
\frac{{\partial}^{2}f}{{\partial\phi}^{2}}+k^{2}f.}}
∂
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}}}
k
𝑘
{\displaystyle{\displaystyle k}}
Identifiers
