Noun
Sturm-Liouville form (plural Sturm-Liouville forms)
(mathematics) the form of a real differential equation expressed as:
d
d
x
[
p
(
x
)
d
y
d
x
]
+
q
(
x
)
y
=
−
λ
w
(
x
)
y
,
{\displaystyle {\frac {d}{dx}}\!\!\left[\,p(x){\frac {dy}{dx}}\right]+q(x)y=-\lambda \,w(x)y,}
for given coefficient functions .mw-parser-output .texhtml{font-family:"Nimbus Roman No9 L","Times New Roman",Times,serif;font-size:118%;line-height:1;white-space:nowrap;font-feature-settings:"lnum","tnum","kern"0;font-variant-numeric:lining-nums tabular-nums;font-kerning:none}.mw-parser-output .texhtml .texhtml{font-size:100%}p(x), q(x), and w(x), an unknown function y = y(x) of the free variable x, and an unknown constant λ.