Degenerate Euler zeta function

TL;DR

This paper introduces the degenerate Euler zeta function, a new holomorphic function linked to degenerate Euler polynomials, expanding the understanding of Euler-related special functions.

Contribution

It defines and studies the properties of the degenerate Euler zeta function, a novel extension of the classical Euler zeta function associated with degenerate Euler polynomials.

Findings

The degenerate Euler zeta function is holomorphic on the complex plane.

It interpolates degenerate Euler polynomials at negative integers.

The paper establishes fundamental properties of this new function.

Abstract

Recently, T. Kim considered Euler zeta function which interpolates Euler polynomials at negative integer (see [3]). In this paper, we study degenerate Euler zeta function which is holomorphic function on complex s-plane associated with degenerate Euler polynomials at negative integers.