A 2n-Point interpolation formula with its applications to q-identities

Based on Krattenthaler's determinantal formula and divided difference operators, we give a 2n-point interpolation formula for a polynomial of degree ≤n in one variable. Several applications of this formula, such as q-identities related to divisor functions, finite forms of the quintuple product identity and a bibasic hypergeometric identity, are discussed. We also give an expansion formula for ∏i=1n(y−uqi−1) by using the supersymmetric complete functions and determinant evaluation.