Some identities involving Bernoulli, Euler and degenerate Bernoulli numbers and their applications

Abstract

The paper has two main objectives. Firstly, it explores the properties of hyperbolic cosine and hyperbolic sine functions by using Volkenborn and the fermionic p-adic integrals, respectively. It also investigates interesting identities involving Bernoulli and degenerate Bernoulli numbers from differential equations with their solutions. Secondly, it introduces a random variable whose mass function is given in terms of Euler polynomials and find some expressions for the expectation of the random variable.

Keywords

• volkenborn integral
• fermionic p-adic integral
• euler numbers
• bernoulli numbers
• degenerate bernoulli numbers
• random variables