  The confluent SUSY QM usually involves a second-order SUSY transformation
where the two factorization energies converge to a single value. In order to
achieve it, one generally needs to solve an indefinite integral, which limits
the actual systems to which it can be applied. Nevertheless, not so long ago,
an alternative method to achieve this transformation was developed through a
Wronskian differential formula [Phys Lett. A 3756 (2012) 692]. In the present
work, we consider the k-confluent SUSY transformation, where k factorization
energies merge into a single value, and we develop a generalized Wronskian
differential formula for this case. Furthermore, we explicitly work out general
formulas for the third- and fourth-order cases and we present as examples the
free particle and the single-gap Lam\'e potentials.
