Probabilistic type 2 Bernoulli and Euler polynomials

Abstract

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.

Keywords

• probabilistic type 2 bernoulli polynomials
• probabilistic type 2 euler polynomials
• probabilistic type 2 cosine-bernoulli polynomials
• probabilistic type 2 sine-bernoulli polynomials
• probabilistic type 2 cosine-euler polynomials
• probabilistic type 2 sine-euler polynomials