Kawashima's relation is conjecturally one of the largest classes of relations among multiple zeta values. Gaku Kawashima introduced and studied a certain Newton series, which we call the Kawashima function, and deduced his relation by establishing several properties of this function. We present a new approach to the Kawashima function without using Newton series. We first establish a generalization of the theory of regularizations of divergent multiple zeta values to Hurwitz type multiple zeta values, and then relate it to the Kawashima function. Via this connection, we can prove a key property of the Kawashima function to obtain Kawashima's relation.

推测地，川岛的关系是多个zeta值之间最大的关系类别之一。Gaku Kawashima引入并研究了某些牛顿级数，我们称其为Kawashima函数，并通过建立该函数的几个属性来推导他的关系。我们提出了一种不使用牛顿级数的川岛函数的新方法。我们首先建立发散的多个zeta值到Hurwitz类型的多个zeta值的正则化理论的一般化，然后将其与Kawashima函数相关联。通过这种联系，我们可以证明川岛函数的关键属性以获得川岛的关系。