Some Properties for Multiple Twisted ( p, q )- L -Function and Carlitz’s Type Higher-Order Twisted ( p, q )-Euler Polynomials

Kyung-Won Hwang and Cheon Seoung Ryoo
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Kyung-Won Hwang: Department of Mathematics, Dong-A University, Busan 49315, Korea
Cheon Seoung Ryoo: Department of Mathematics, Hannam University, Daejeon 34430, Korea

Mathematics, 2019, vol. 7, issue 12, 1-12

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.

Keywords: higher order twisted ( p , q )-Euler numbers and polynomials; q-L-function; multiple twisted ( p , q )-L-function; symmetric identities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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