Some identities of the degenerate Krawtchouk polynomials

In this paper, we introduce a novel class of degenerate Krawtchouk polynomials associated with degenerate Pascal random variables characterized by parameters r > 0 and q ? (0, 1). We derive a variety of new identities involving these polynomials, particularly focusing on combinatorial identities linked to the n-th moments of the degenerate Pascal distribution, as well as their connections to special numbers and polynomials. Furthermore, we extend our framework to define and investigate a two-parameter gen-eralization, referred to as the two-variable degenerate Krawtchouk polynomials, arising from degenerate Pascal random variables with parameters q and ?. We explore the algebraic and analytic properties of these polynomials and establish their relationships with the central moments of the associated distributions, as well as with various classes of special numbers and polynomials.