(alpha)-Difference Operator and Its Application on Number Theory

摘要

In this paper, the authors define the generalized? (alpha)-difference operator (Delta_{alpha(ell)}) for positive real $ell$ and obtain formulae on the sums? of products of (k^m), (k_ell^{(m)}) and powers of (alpha)? using inverse operator (Delta_{alpha(ell)}^{-1}). Suitable examples are provided to illustrate the main results.