Summation Formula Related To Extended a-Delta Operators

The paper 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.