Double Sums of the Szasz Sequence

Abstract

This study introduced and investigated a modification of the Szasz sequence in double sums with one variable. This sequence's recurrence relation for the m-th order moment, convergence theorem, and Voronovskaya-type asymptotic theorem in ordinary approximation are investigated. A numerical example is also provided to demonstrate the approximation of the chosen test function by this modification sequence, and the numerical results are compared to the numerical results of the classical Szasz sequence. It turns out that the results achieved from the modification sequence are superior to those obtained from the classical sequence.