On analogues of Arakawa-Kaneko zeta functions of Mordell-Tornheim type

TL;DR

This paper introduces analogues of Arakawa-Kaneko zeta functions, establishes their functional relations with Mordell-Tornheim multiple zeta functions, and derives new formulas among Mordell-Tornheim zeta values.

Contribution

It constructs new analogues of Arakawa-Kaneko zeta functions and explores their connections with Mordell-Tornheim multiple zeta functions, providing novel formulas.

Findings

Established functional relations between the new zeta functions and Mordell-Tornheim functions.

Derived new formulas among Mordell-Tornheim multiple zeta values.

Extended the theory of multiple zeta functions with new analogues.

Abstract

In this paper, we construct certain analogues of the Arakawa-Kaneko zeta functions. We prove functional relations between these functions and the Mordell-Tornheim multiple zeta functions. Furthermore we give some formulas among Mordell-Tornheim multiple zeta values as their applications.