Abstract
Kim and Kim (Russ. J. Math. Phys. 26, 2019, 40-49) introduced polyexponential function as an inverse to the polylogarithm function and by this, constructed a new type poly-Bernoulli polynomials. Recently, by using the polyexponential function, a number of generalizations of some polynomials and numbers have been presented and investigated. Motivated by these researches, in this paper, multi-poly-Euler polynomials are considered utilizing the degenerate multiple polyexponential functions and then, their properties and relations are investigated and studied. That the type 2 degenerate multi-poly-Euler polynomials equal a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind is proved. Moreover, an addition formula and a derivative formula are derived. Furthermore, in a special case, a correlation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers is shown.
Highlights
We introduce a novel class of degenerate multi-poly-Euler polynomials and numbers utilizing the degenerate multi-polyexponential function and studied their main explicit relations and identities
We investigate some properties of the type 2 degenerate multi-poly-Euler polynomials
A summation formula for the type 2 degenerate multi-poly-Euler polynomials is stated in the following theorem
Summary
Special functions have recently been applied in numerous fields of applied and pure mathematics besides in such other disciplines as physics, economics, statistics, probability theory, biology and engineering, cf. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26], and see the references cited therein. Kim and Kim [15] considered degenerate poly-Bernoulli polynomials by means of the degenerate polylogarithm function and investigated several properties and relations. Kim and Kim [18] considered a new type degenerate Bell polynomials via degenerate polyexponential functions and gave some of their properties. Kim et al [20] introduced degenerate multiple polyexponential functions whereby the degenerate multi-poly-Genocchi polynomials are considered and multifarious explicit expressions and some properties were investigated. Studied a new type of type 2 poly-Euler polynomials and its degenerate form by utilizing the modified polyexponential function. We introduce a novel class of degenerate multi-poly-Euler polynomials and numbers utilizing the degenerate multi-polyexponential function and studied their main explicit relations and identities. The last section outlines finding gains and the conclusions in this work and mentions recommendations for future studies
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