Abstract
The main goal of this paper is to study some interesting identities for the multiple twisted ( p , q ) -L-function in a complex field. First, we construct new generating functions of the new Carlitz-type higher order twisted ( p , q ) -Euler numbers and polynomials. By applying the Mellin transformation to these generating functions, we obtain integral representations of the multiple twisted ( p , q ) -Euler zeta function and multiple twisted ( p , q ) -L-function, which interpolate the Carlitz-type higher order twisted ( p , q ) -Euler numbers and Carlitz-type higher order twisted ( p , q ) -Euler polynomials at non-positive integers, respectively. Second, we get some explicit formulas and properties, which are related to Carlitz-type higher order twisted ( p , q ) -Euler numbers and polynomials. Third, we give some new symmetric identities for the multiple twisted ( p , q ) -L-function. Furthermore, we also obtain symmetric identities for Carlitz-type higher order twisted ( p , q ) -Euler numbers and polynomials by using the symmetric property for the multiple twisted ( p , q ) -L-function.
Highlights
Many researchers have studied the Bernoulli numbers and polynomials, Euler numbers and polynomials, Genocchi numbers and polynomials, tangent numbers and polynomials, zeta function, and Hurwitz zeta function
Ryoo [7] discussed generalized Barnes-type multiple q-Euler polynomials twisted by use of the roots of unity
We introduce the multiple twisted ( p, q)-L-function in the complex field and Carlitz-type higher order twisted ( p, q)-Euler numbers and polynomials
Summary
Many researchers have studied the Bernoulli numbers and polynomials, Euler numbers and polynomials, Genocchi numbers and polynomials, tangent numbers and polynomials, zeta function, and Hurwitz zeta function. We introduce the multiple twisted ( p, q)-L-function in the complex field and Carlitz-type higher order twisted ( p, q)-Euler numbers and polynomials. We give symmetric identities for Carlitz-type higher order twisted ( p, q)-Euler numbers and polynomials by using the symmetric property for the multiple twisted ( p, q)-L-function.
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