Truncated euler polynomials

Abstract

We define a truncated Euler polynomial Em,n(x) as a generalization of the classical Euler polynomial En(x). In this paper we give its some properties and relations with the hypergeometric Bernoulli polynomial.

On Degenerate Truncated Special Polynomials

“…In particular, the family of special polynomials is one of the most useful and applicable family of special functions. Some of the most considerable polynomials in the theory of special polynomials are the Fubini polynomials (see [9,[15][16][17]36]), the Bernoulli polynomials (see [2,[5][6][7]11,13,29,[31][32][33][34][35]), the Euler polynomials (see [2,[5][6][7]11,27,29,[31][32][33][34][35]), the Bernstein polynomials (see [1,20]) and the Bell polynomials (see [3,4,18,19,[22][23][24][25]). Recently, the aforementioned polynomials and their several extensions have been densely studied and investigated by diverse mathematicians and physicists and see also each of the references cited therein.…”

Truncated Fubini Polynomials

“…see [1][2][3][4][5][6][7][8][9][10] for details about the aforesaid polynomials. The Bernoulli numbers B n and Euler numbers E n are obtained by the special cases of the corresponding polynomials at x = 0, namely: B n (0) := B n and E n (0) := E n .…”

“…Recently, several mathematicians have studied truncated-type special polynomials such as truncated Bernoulli polynomials and truncated Euler polynomials; cf. [1,4,7,9,11,12].…”

“…The Stirling numbers of the second kind are given by the following exponential generating function: [2][3][4][5]7,8,10,13]…”

“…where the notation (x) µ called the falling factorial equals [2][3][4][5][7][8][9][10]13], and see also the references cited therein. The Apostol-type Stirling numbers of the second kind is defined by (cf.…”