Modified Clebsch-gordan-type Expansions for Products of Discrete Hypergeometric Polynomials. 1

Starting from the second-order diierence hypergeometric equation satissed by the set of discrete orthogonal polynomials fp n g, we nd the analytical expressions of the expansion coeecients of any polynomial r m (x) and of the product r m (x)q j (x) in series of the set fp n g. These coeecients are given in terms of the polynomial coeecients of the second-order diierence equations satissed by the involved discrete hypergeometric polynomials. Here q j (x) denotes an arbitrary discrete hypergeometric polynomial of degree j. The particular cases in which fr m g corresponds to the non-orthogonal families fx m g, the rising factorials or Pochhammer polynomials f(x) m g and the falling factorial or Stirling polynomials fx m] g are considered in detail. The connection problem between discrete hypergeometric polynomials, which here corresponds to the product case with m = 0, is also studied and its complete solution for all the classical discrete orthogonal hypergeometric (CDOH) polynomials is given. Also, the inversion problems of CDOH polynomials associated to the three aforementioned non-orthogonal families are solved.