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Open AccessArticle

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

1
Department of Mathematics, Dong-A University, Busan 49315, Korea
2
Department of Mathematics, Hannam University, Daejeon 34430, Korea
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1205; https://doi.org/10.3390/math7121205
Received: 7 November 2019 / Revised: 29 November 2019 / Accepted: 5 December 2019 / Published: 9 December 2019
(This article belongs to the Special Issue Complex Analysis and Its Applications 2019)
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. View Full-Text
Keywords: higher order twisted (p, q)-Euler numbers and polynomials; q-L-function; multiple twisted (p, q)-L-function; symmetric identities higher order twisted (p, q)-Euler numbers and polynomials; q-L-function; multiple twisted (p, q)-L-function; symmetric identities
MDPI and ACS Style

Hwang, K.-W.; Ryoo, C.S. Some Properties for Multiple Twisted (p, q)-L-Function and Carlitz’s Type Higher-Order Twisted (p, q)-Euler Polynomials. Mathematics 2019, 7, 1205.

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