Zeros of difference polynomials (Q1185252)

Studies --- both analytic and numerical --- on polynomials have been of immense interest for long. Here the authors deal in detail with various questions relating to the zeros of difference polynomials. Particularly, defining the difference operator by \(\Delta f(x)=f(x+1)-f(x)\), the polynomial \(\Delta^ mx^ n\) of degree \((n-m)\) having \((n-m)\) collinear zeros, is treated. A reduced central difference polynomial \(C(z)\) is constructed, which in turn, is investigated with reference to: i) bounds for spectral radius, ii) expansions of zeros and iii) conjectures with observations on the zeros. Two tables and a graph add to the value of the paper.