A q-analogue of Boyadzhiev-Mneimneh-type binomial sums of finite multi-polylogarithms

2025/10/29 by Kamano, Ken
#11M32 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.25059

Abstract

We give a formula for a q-analogue of Boyadzhiev-Mneimneh-type binomial sums of finite multi-polylogarithms. In the limit as q→ 1, this formula reduces to an identity equivalent to the Sakugawa-Seki identities. We also give a formula for Boyadzhiev-Mneimneh-type sums corresponding to the Cauchy binomial theorem.

Citations

• Pan-Xu conjecture and reduction formulas for polylogarithms
• Mneimneh-type Binomial Sums of Multiple Harmonic-type Sums
• Ohno-type identities for multiple harmonic sums
• On functional equations of finite multiple polylogarithms
• Newton series and extended derivation relations for multiple L-values
• A q-analogue of a formula of Hernandez obtained by inverting a result of Dilcher

Related

• Mneimneh-type Binomial Sums of Multiple Harmonic-type Sums
• On alternating sums of binomial coefficients and q-binomial coefficients
• Pan-Xu conjecture and reduction formulas for polylogarithms
• Discovering and Proving Infinite Binomial Sums Identities
• Shuffle product of finite multiple polylogarithms