On Monomial Deformations of Generalized Delsarte Polynomials

Abstract

By a generalized Delsarte polynomial we mean a Laurent polynomial whose exponent vectors are linearly independent. We consider certain monomial deformations of generalized Delsarte polynomials and study their associated differential modules. We determine the solutions at the origin, which are all classical ${}_kF_{k-1}$-hypergeometric functions with the variable raised to a power. Using standard changes of variable, we also obtain the solutions at infinity.