Some Identities of the Degenerate Krawtchouk polynomials

Abstract

In this study, we introduce a new type of degenerate Krawtchouk polynomials associated with degenerate Pascal random variables with parameters r > 0 and q ∈]0, 1[ and we derive some interesting identities related combinatorial identities related with the n-th moment of the degenerate Pascal random
variable, special numbers and polynomials. Additionally, we delve into the discussion of the degenerate polynomials associated with degenerate Pascal random variables with two parameters q and α, called the two variable degenerate Krawtchook polynomials. We show their connection with the degenerate Pascal central moments, special numbers and polynomials.