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

Author

Listed:
  • Kyung-Won Hwang

    (Department of Mathematics, Dong-A University, Busan 49315, Korea)

  • Cheon Seoung Ryoo

    (Department of Mathematics, Hannam University, Daejeon 34430, Korea)

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.

Suggested Citation

  • Kyung-Won Hwang & Cheon Seoung Ryoo, 2019. "Some Properties for Multiple Twisted ( p , q )- L -Function and Carlitz’s Type Higher-Order Twisted ( p , q )-Euler Polynomials," Mathematics, MDPI, vol. 7(12), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1205-:d:295661
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