Extended q-euler numbers and polynomials associated with fermionic p-adic q-integral on Z p

Abstract

In this paper, we investigate some properties between q-Bernstein polynomials and q-Euler numbers by using fermionic p-adic q-integrals on Z p . From these properties, we derive some interesting identities related to the q-Euler numbers.1 q , (see [2]).

Construction of q-discrete two-dimensional Toda lattice equation with self-consistent sources

“…In [7,10], Kim studied the p−adic L−function L p (s, χ) which interpolates Bernoulli numbers at negative integers. Kim [4] constructed a new q-extension of generalized Bernoulli polynomials attached to χ and proved the existence of a specific p-adic interpolation function that interpolates the q-extension of generalized Bernoulli polynomials at negative integers. The p-adic q-integral ( or q-Volkenborn integral) was originally constructed by T. Kim [7,10 ], who indicated a connection between the q-integral and non-archimedean combinatorial analysis.…”

Some results for the q-Bernoulli, q-Euler numbers and polynomials

“…From that time on these and other related subjects have been studied by various authors (see, e.g., [3][4][5][6][7][8][9][10]). Many recent studies on q-analogue of the Bernoulli, Euler numbers, and polynomials can be found in Choi et al [11], Kamano [3], Kim [5,6,12], Luo [7], Satoh [9], Simsek [13,14] and Tsumura [10].…”

IDENTITIES OF SYMMETRY FOR THE HIGHER ORDER q-BERNOULLI POLYNOMIALS

“…where B n (x) and E n (x) are the Bernoulli and Euler polynomials, respectively, for details of the above formulas, we refer to [11,13,15,17,25]. The multiple Volkenborn integrals considered in this paper are all computable by iterated integrations.…”