The factorization method to solve ordinary differential equations due to Darboux has many applications to orthogonal polynomials and quantum mechanics. The authors propose an extension to
-difference equations. It is a
-analogue, since, in the continuous limit
, it boils down to the classical factorization method (at least in the usual intuitive description of “continuous limit”). The paper contains the proof in a particular important case (indeed, a generalisation of a famous study by L. Infeld
and T. E. Hull
, Rev. Mod. Phys. 23, 21–68 (1951; Zbl 0043.38602
) that the
-Hahn orthogonal polynomials are among the solutions. They also consider other interesting examples.