Newton series and extended derivation relations for multiple $L$-values

TL;DR

This paper explores Newton series for truncated multiple $L$-values and introduces extended derivation relations, providing new insights and relations in the study of multiple $L$-values.

Contribution

It presents a novel formulation of Newton series for truncated multiple $L$-values and proves extended derivation relations, advancing the theoretical understanding of multiple $L$-values.

Findings

Derived new relations for multiple $L$-values using Newton series

Formulated and proved extended derivation relations for multiple $L$-values

Enhanced the theoretical framework for studying multiple $L$-values

Abstract

We investigate Newton series for truncated multiple $L$-values and thereby obtain a class of relations for multiple $L$-values. In addition, we give a formulation and a proof of extended derivation relations for multiple $L$-values.