Stirling polynomials and multiple zeta (star) functions at non-positive integers
Abstract
It is known that the directional limit values of multiple zeta functions (MZFs) at non-positive integers can be expressed by Bernoulli numbers. This paper gives explicit formulas for the reverse values of MZFs and multiple zeta star functions (MZSFs) at non-positive integers using Stirling polynomials. We also study the following two points. A connection between MZFs and MZSFs at non-positive integers and a connection between reverse values and generalized Gregory coefficients studied by Matsusaka, Murahara, and Onozuka.
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Combinatorial Mathematics
Mathematical functions and polynomials
Publication details
- Journal / source
- The Ramanujan Journal
- Publisher
- Springer Science and Business Media LLC
- Volume
- 69
- Issue
- 3
- Publication date
- 27 February 2026
- Language
- EN