  We show that the coefficients of the three-term recurrence relation for
orthogonal polynomials with respect to a semi-classical extension of the
Laguerre weight satisfy the fourth Painlev\'e equation when viewed as functions
of one of the parameters in the weight. We compare different approaches to
derive this result, namely, the ladder operators approach, the isomonodromy
deformations approach and combining the Toda system for the recurrence
coefficients with a discrete equation. We also discuss a relation between the
recurrence coefficients for the Freud weight and the semi-classical Laguerre
weight and show how it arises from the B\"acklund transformation of the fourth
Painlev\'e equation.
