Abstract
In this paper we define the degenerate Carlitz-type ( p , q ) -Euler polynomials by generalizing the degenerate Euler numbers and polynomials, degenerate Carlitz-type q-Euler numbers and polynomials. We also give some theorems and exact formulas, which have a connection to degenerate Carlitz-type ( p , q ) -Euler numbers and polynomials.
Highlights
Many researchers have studied about the degenerate Bernoulli numbers and polynomials, degenerate Euler numbers and polynomials, degenerate Genocchi numbers and polynomials, degenerate tangent numbers and polynomials
We remind that the classical degenerate Euler numbers En (λ) and Euler polynomials En ( x, λ), which are defined by generating functions like (1), and (2)
Let w2 = 1 in Theorem 6, we have the multiplication theorem for the degenerate Carlitz-type ( p, q)-Euler polynomials
Summary
Many researchers have studied about the degenerate Bernoulli numbers and polynomials, degenerate Euler numbers and polynomials, degenerate Genocchi numbers and polynomials, degenerate tangent numbers and polynomials (see [1,2,3,4,5,6,7]). Some generalizations of the Bernoulli numbers and polynomials, Euler numbers and polynomials, Genocchi numbers and polynomials, tangent numbers and polynomials are provided (see [6,8,9,10,11,12,13]). We remind that the classical degenerate Euler numbers En (λ) and Euler polynomials En ( x, λ), which are defined by generating functions like (1), and (2) (see [1,2]). The numbers S2 (n, m) is like this tn ( e t − 1) m n!
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