# A Note on Kawashima Functions

## TL;DR

This paper surveys Kawashima functions, highlighting their generalization of the digamma function and exploring their applications to multiple zeta values and related formulas.

## Contribution

It provides a comprehensive overview of Kawashima functions and connects their properties to multiple zeta values and recent research developments.

## Key findings

- Kawashima functions generalize the digamma function.
- Various formulas for the digamma function are extended to Kawashima functions.
- Connections between Kawashima functions and multiple zeta value relations are discussed.

## 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.