A Note on Kawashima Functions

2017/02/05 by Shûji Yamamoto, Yamamoto, Shuji
Mathematics · #11M32 #33B15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1702.01377

openalex publication_date 2017/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note is a survey of results on the function F_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 ψ(z), and explain how various formulas for ψ(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.

Citations

• Multiple series expressions for the Newton series which interpolate finite multiple harmonic sums

Related

• A generalized regularization theorem and Kawashima's relation for multiple zeta values
• ℚ-linear relations of specific families of multiple zeta values and the linear part of Kawashima's relation
• On an analog of the Arakawa-Kaneko zeta function and relations of some multiple zeta values
• Quadratic relations for a q-analogue of multiple zeta values
• Multitangent functions and symmetric multiple zeta values