2D-Fibonacci Summation with Extorial Functions

In this paper, we derive the second-order Fibonacci summation formula for the product of polynomial and extorial functions using the two-dimensional second-order Fibonacci nabla difference operator, its inverse, and the two-dimensional second-order Fibonacci numbers. The function obtained by substituting polynomial with factorial polynomial in the expansion of the exponential function is referred to as the extorial function. We also discuss the properties of the extorial function in this chapter. Additionally, we apply the extorial function to two-dimensional difference equations