Simple proof of the functional relation for the Lerch type Tornheim double zeta function

TL;DR

This paper provides a straightforward proof of the functional relation for the Lerch type Tornheim double zeta function, enabling simpler derivations of explicit formulas for double L-values.

Contribution

It introduces a simple proof technique for the functional relation, facilitating easier evaluation of double L-values compared to previous methods.

Findings

Simplified proof of the functional relation.

Explicit evaluation formulas for double L-values derived.

Enhanced understanding of the Lerch type Tornheim double zeta function.

Abstract

In this paper, we give a simple proof of the functional relation for the Lerch type Tornheim double zeta function. By using it, we obtain simple proofs of some explicit evaluation formulas for double $L$-values.