Combinatorial aspects of the Baker-Akhiezer functions for S2

We show here that a certain sequence of polynomials arising in the study of S2 m-quasi invariants satisfies a 3-term recursion. This leads to the discovery that these polynomials are closely related to the Bessel polynomials studied by Luc Favreau. This connection reveals a variety of combinatorial properties of the sequence of Baker–Akhiezer functions for S2. In particular we obtain in this manner their generating function and show that it is equivalent to several further identities satisfied by these functions. © 2003 Published by Elsevier Ltd