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

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

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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 read more interesting identities involving Bernoulli and degenerate Bernoulli numbers from differential fleshlight automatique 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.