A Note on Kawashima Functions

Abstract

This note is a survey of results on the function $F_{\mathbf{k}}(z)$ introduced by G. Kawashima, and its applications to the study of multiple zeta values. We stress the viewpoint that the Kawashima function is a generalization of the digamma function $\psi(z)$, and explain how various formulas for $\psi(z)$ are generalized. We also discuss briefly the relationship of the results on the Kawashima functions with a recent work on Kawashima's MZV relation by M. Kaneko and the author.