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In this paper, we introduce the so-called elliptic Askey-Wilson polynomialswhich are homogeneous polynomials in two special theta functions. With regardto the significance of polynomials of such kind, we establish some generalelliptic interpolation formulas by the methods of matrix inversions and ofpolynomial representations. Furthermore, we find that the basis of ellipticinterpolation space due to Schlosser can be uniquely characterized via theelliptic Askey-Wilson polynomials. As applications of these ellipticinterpolation formulas, we establish some new elliptic function identities,including an extension of Weierstrass' theta identity, a generalized ellipticKarlsson-Minton type identity, and an elliptic analogue of Gasper's summationformula for very-well-poised ${}_{6+2m}\phi_{5+2m}$ series.

Further study on elliptic interpolation formulas for the elliptic Askey-Wilson polynomials and allied identities