On the new type of degenerate poly-Genocchi numbers and polynomials

[摘要] Kim and Kim (J. Math. Anal. Appl. 487:124017, 2020) introduced the degenerate logarithm function, which is the inverse of the degenerate exponential function, and defined the degenerate polylogarithm function. They also studied a new type of the degenerate Bernoulli polynomials and numbers by using the degenerate polylogarithm function. Motivated by their research, we subdivide this paper into two parts. In Sect. 2, we construct a new type of degenerate Genocchi polynomials and numbers by using the degenerate polylogarithm function, called the degenerate poly-Genocchi polynomials and numbers, deriving several combinatorial identities related to the degenerate poly-Genocchi numbers and polynomials. Then, in Sect. 3, we also consider the degenerate unipoly Genocchi polynomials attached to an arithmetic function by using the degenerate polylogarithm function. In particular, we provide some new explicit computational identities of degenerate unipoly polynomials related to special numbers and polynomials.

[学科分类] 航空航天科学

[关键词] Degenerate poly-Genocchi numbers and polynomials;Degenerate polylogarithm functions;Degenerate Bernoulli numbers and polynomials;Degenerate Euler numbers and polynomials;Degenerate unipoly functions;Degenerate unipoly Genocchi polynomials