Studies On Several Properties Of The Genocchi Numbers And Polynomials

Combing A.Genocchi’s definition of the Genocchi numbers in 1852,L.Carlitz’s definition of the degenerate Bernoulli numbers in 1956,M.Kaneko’s definition of polyBernoulli numbers in 1999 and T.Kim et al.’s definition of fully degenerate poly-Bernoulli polynomials in 2016,in this paper,we introduce the notions of the fully degenerate poly-Genocchi polynomials,the degenerate sine-Genocchi polynomials,the degenerate cosine-Genocchi polynomials,the type 2 degenerate Genocchi polynomials,the type 2degenerate sine-Genocchi polynomials and cosine-Genocchi polynomials,we also investigate their properties and prove several combinatorial identities of them including the classical Genocchi numbers by using the generating function method.