Identities Involving Two Kinds of q-Euler Polynomials and Numbers
Département de Mathématiques
Université d'Evry Val d'Essonne
Bâtiment I.B.G.B.I., 3ème étage
23 Bd. de France
91037 Evry Cedex
Faculty of Engineering Science
3-3-35 Yamate-cho, Suita-shi
We introduce two kinds of q-Euler polynomials and numbers,
and investigate many of their interesting properties.
In particular, we establish q-symmetry properties of these
q-Euler polynomials, from which we recover the so-called
Kaneko-Momiyama identity for the ordinary Euler polynomials,
discovered recently by Wu, Sun, and Pan. Indeed,
a q-symmetry and q-recurrence formulas among sum of product
of these q-analogues Euler numbers and polynomials are obtained.
As an application, from these q-symmetry formulas
we deduce non-linear recurrence formulas for the product of the
ordinary Euler numbers and polynomials.
Full version: pdf,
Received February 15 2012;
revised version received March 31 2012.
Published in Journal of Integer Sequences, April 9 2012.
Journal of Integer Sequences home page