Summation Formula Related To Extended α-Delta Operators

Abstract

This research aims to develop higher-order discrete fundamental theorems for delta
and alpha-delta operators. By equating the closed and summation forms of inverse
operators, we derive novel summation formulae. Additionally, we establish
comprehensive summation formulae for generalized exponential and extorial
functions incorporating shift values. These advancements contribute to a deeper
understanding of the discrete calculus framework and its applications across
various mathematical and scientific fields. The results obtained can be applied to
improve discrete dynamic systems, enhance computational techniques and provide
new insights into the behavior of discrete functions. Our findings pave the way for
further exploration and potential breakthroughs in discrete mathematics and its
interdisciplinary applications.