## Fredholm integral equations and the resolvent kernel

Consider the *inhomogeneous Fredholm integral equation*:

\[ H \psi(\mu) = \lambda \int_a^b \sigma(\mu, \mu') \psi(\mu') d\mu'
+ S(\mu) \]

The unknown to be solved for is \(\psi(\mu)\) where \(a \le \mu \le b\) is the
independent variable, and the known function \(\sigma(\mu, \mu')\) is known as
the *kernel*. This is an *inhomogeneous* equation because the known function
\(S(\mu) \ne 0\).