标题： 阿拉克瓦-神谷多重zeta函数与欧拉-扎吉尔类型之间的显式公式 显示英文标题

标题： Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types

摘要： 多重阿拉卡瓦-神保型和欧拉-扎吉尔型的多重zeta函数被认为是黎曼zeta函数的推广。 在2018年，神保和田村证明了阿拉卡瓦-神保型的多重zeta函数可以表示为${\mathbb Q}$线性组合，即欧拉-扎吉尔型的乘积和多重zeta值的乘积。 在本文中，我们给出了上述关系的显式公式。 此外，作为其证明的关键，我们还显式地给出了多polylogarithm函数之间的某些函数方程。 显示英文摘要

摘要： Multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types are known as generalizations of the Riemann zeta function. In 2018, Kaneko and Tsumura proved that the multiple zeta functions of Arakawa-Kaneko type can be expressed as a ${\mathbb Q}$-linear combination of products of the ones of Euler-Zagier type and multiple zeta values. In this paper, we give explicit formulas to the above mentioned relation. Moreover, as a key of its proof, we also give certain functional equations among multi-polylogarithm functions explicitly.