Abstract
The main object of this paper is to introduce a new class of Laguerre-based poly-Genocchi polynomials and investigate some properties for these polynomials and related to the Stirling numbers of the second kind. We derive summation formulae and general symmetry identities by using different analytical means and applying generating functions.
Highlights
The generalized Bernoulli, Euler and Genocchi polynomials of order α are usually defined by means of the following generating functions: t et − 1 α ext = ∞ Bn(α)(x) tn n! (| t |< 2π; = 1), n=0 (1.1)
The main object of this paper is to introduce a new class of Laguerre-based poly-Genocchi polynomials and investigate some properties for these polynomials and related to the Stirling numbers of the second kind
The poly-Bernoulli numbers and polynomials are defined by following generating functions
Summary
The poly-Bernoulli numbers and polynomials are defined by following generating functions The poly-Genocchi numbers and polynomials are defined by following generating functions (see [14]): 2Lik(1 − e−t) et + 1 Let k ∈ Z, we inroduce 2-variable Laguerre-based poly-Genocchi polynomials by the following generating function: so that Where LGn(x, y) is Laguerre-based Genocchi polynomials (see [13]).
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