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A note on Kawashima functions
Shuji Yamamoto1
1 Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan
Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2019), pp. 151-163.

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 the recent work on Kawashima’s MZV relation by M. Kaneko and the author.

L’objet de cette note est de faire une revue des résultats sur la fonction F k (z) définie par G. Kawashima et des applications à l’étude des valeurs de fonctions zêtas multiples. Nous mettons l’accent sur le fait que cette fonction de Kawashima est une généralisation de la fonction digamma ψ(z) et nous expliquons comment des formules valables pour ψ(z) se généralisent. Nous survolons également les liens entre les résultats sur les fonctions de G. Kawashima avec les travaux récents des relations MZV de Kawashima de M. Kaneko et de l’auteur.

Published online:
DOI: 10.5802/pmb.38
Classification: 11M32, 33B15
Keywords: Kawashima functions, Digamma function, Polygamma functions, Multiple zeta values

Shuji Yamamoto 1

1 Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Shuji Yamamoto. A note on Kawashima functions. Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2019), pp. 151-163. doi : 10.5802/pmb.38. https://pmb.centre-mersenne.org/articles/10.5802/pmb.38/

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