A functional equation for multiple zeta functions and generalized confluent hypergeometric functions

Anju Yokoi

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arXiv · 2510.04444

A functional equation for multiple zeta functions and generalized confluent hypergeometric functions

Anju Yokoi

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Abstract

In this paper, we introduce a new function, the multiple confluent hypergeometric functions, and establish a functional equation for the $r$-variable Euler--Zagier multiple zeta functions using it. In the case when $r=2$, this functional equation includes the well-known functional equation for the Euler--Zagier double zeta functions obtained by Matsumoto.

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Anju Yokoi. 2025-10-06. A functional equation for multiple zeta functions and generalized confluent hypergeometric functions. https://arxiv.org/abs/2510.04444

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