The Sturm-Liouville Theory

[Void123]

Homework Statement

Find the weight functions for Trigg's, Legendre's, Legendre's Associated, and Bessel's equations.

Homework Equations

Not sure.

The Attempt at a Solution

I know that the weight function, $$\omega(x)$$, is real and correlates to the scalar product of functions.

Thanks.

 

[lanedance]

the weight function determines how functions are othogonal & magnitudes by defining the inner product:

$$<f(x),g(x)> = \int dx.g(x)f(x)w(x)$$

if i remember correctly, by writing the DE in the correct SL form, the weight functio nshoudl be reasonably apparent