PROBABILISTIC DEGENERATE BERNOULLI AND EULER POLYNOMIALS OF COMPLEX VARIABLE

Let [Formula: see text] be a random variable whose moment generating function exists in a neighborhood of the origin. Recently, the degenerate Euler (Bernoulli) polynomials of complex variable have been studied. In this paper, as probabilistic extensions of those polynomials, we study the probabilistic degenerate Euler (Bernoulli) polynomials of complex variable associated with [Formula: see text]. In addition, we investigate probabilistic extensions of the degenerate cosine-Euler (sine-Euler) polynomials, the degenerate cosine-Bernoulli (sine-Bernoulli) polynomials and the degenerate cosine (sine) polynomials. The aim of this paper is to derive several fundamental properties, identities and explicit expressions for those probabilistic extensions of special polynomials by using generating functions.