1,563 research outputs found
On a class of -Bernoulli, -Euler and -Genocchi polynomials
The main purpose of this paper is to introduce and investigate a class of
-Bernoulli, -Euler and -Genocchi polynomials. The -analogues of
well-known formulas are derived. The -analogue of the Srivastava--Pint\'er
addition theorem is obtained. Some new identities involving -polynomials are
proved
Note on q-extensions of Euler numbers and polynomials of higher order
In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order
twisted -extension of Euler polynomials and numbers, by using -adic
q-deformed fermionic integral on . By applying their generating
functions, they derived the complete sums of products of the twisted
-extension of Euler polynomials and numbers, see[13, 14]. In this paper
we cosider the new -extension of Euler numbers and polynomials to be
different which is treated by Ozden-Simsek-Cangul. From our -Euler numbers
and polynomials we derive some interesting identities and we construct
-Euler zeta functions which interpolate the new -Euler numbers and
polynomials at a negative integer. Furthermore we study Barnes' type -Euler
zeta functions. Finally we will derive the new formula for " sums products of
-Euler numbers and polynomials" by using fermionic -adic -integral on
.Comment: 11 page
- β¦