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Assume that the moment-generating function of the random variable Y exists in a neighborhood of the origin. The aim of this paper is to investigate the probabilistic type 2 Bernoulli polynomials associated with Y and the probabilistic type 2 Euler polynomials associated with Y, along with the probabilistic type 2 cosine-Bernoulli polynomials associated with Y, the probabilistic type 2 sine-Bernoulli polynomials associated with Y, the probabilistic type 2 cosine-Euler polynomials associated with Y, and the probabilistic type 2 sine-Euler polynomials associated with Y. We deal with their properties, related identities and explicit expressions.
Chen et al. (Mon,) studied this question.