A -Point interpolation formula with its applications to -identities

Based on Krattenthaler’s determinantal formula and divided difference operators, we give a 2 n -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 = 1 n ( y − u q i − 1 ) by using the supersymmetric complete functions and determinant evaluation.