2016 Elsevier B.V. All rights reserved. Bivariate Gonarov polynomials are a basis of the solutions of the bivariate Gonarov Interpolation Problem in numerical analysis. A sequence of bivariate Gonarov polynomials is determined by a set of nodes Z={( xi,j , yi,j ) R2 } and is an affine sequence if Z is an affine transformation of the lattice grid N2 , i.e., ( xi,j , yi,j )T=A(i,j) T +( c1 , c2 ) T for some 22 matrix A and constants c1 , c2 . In this paper we prove that a sequence of bivariate Gonarov polynomials is of binomial type if and only if it is an affine sequence with c1 = c2 =0. Such polynomials form a higher-dimensional analog of the Abel polynomial An (x;a)=x (x-an)n-1 . We present explicit formulas for a general sequence of bivariate affine Gonarov polynomials and its exponential generating function, and use the algebraic properties of Gonarov polynomials to give some new two-dimensional generalizations of Abel identities.
