2017/10/11 by Zhonghua Li, Li, Zhonghua, Noriko Wakabayashi +1
Mathematics · #05A30 #11B65 #11M32 #33D15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1710.04025
openalex publication_date 2017/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Interpolated multiple q-zeta values are deformation of multiple q-zeta values with one parameter, t, and restore classical multiple zeta values as t = 0 and q → 1. In this paper, we discuss generating functions for sum of interpolated multiple q-zeta values with fixed weight, depth and i-height. The functions are systematically expressed in terms of the basic hypergeometric functions. Compared with the result of Ohno and Zagier, our result includes three generalizations: general height, q-deformation and t-interpolation. As an application, we prove some expected relations for interpolated multiple q-zeta values including sum formulas.