Some Symmetry Identities for Carlitz’s Type Degenerate Twisted (<i>p</i>,<i>q</i>)-Euler Polynomials Related to Alternating Twisted (<i>p</i>,<i>q</i>)-Sums

Abstract

In this paper, we define a new form of Carlitz’s type degenerate twisted (p,q)-Euler numbers and polynomials by generalizing the degenerate Euler numbers and polynomials, Carlitz’s type degenerate q-Euler numbers and polynomials. Some interesting identities, explicit formulas, symmetric properties, a connection with Carlitz’s type degenerate twisted (p,q)-Euler numbers and polynomials are obtained. Finally, we investigate the zeros of the Carlitz’s type degenerate twisted (p,q)-Euler polynomials by using computer.

Keywords

• degenerate Euler numbers and polynomials
• degenerate <i>q</i>-Euler numbers and polynomials
• Carlitz’s type degenerate twisted (<i>p</i>,<i>q</i>)-Euler numbers and polynomials
• alternating twisted (<i>p</i>,<i>q</i>)-sums