Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
149 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Multiple zeta values and Euler sums (1609.05863v3)

Published 16 Sep 2016 in math.NT

Abstract: In this paper, we establish some expressions of series involving harmonic numbers and Stirling numbers of the first kind in terms of multiple zeta values, and present some new relationships between multiple zeta values and multiple zeta star values. The relationships obtained allow us to find some nice closed form representations of nonlinear Euler sums through Riemann zeta values and linear sums. Furthermore, we show that the combined sums [H\left( {a,b;m,p} \right) := \sum\limits_{a + b = m - 1} {\zeta \left( {{{\left{ p \right}}a},p + 1,{{\left{ p \right}}_b}} \right)}\quad (m\in \N,p>1) ] and [{H^ \star }\left( {a,b;m,p} \right) := \sum\limits{a + b = m - 1} {{\zeta ^ \star }\left( {{{\left{ p \right}}_a},p + 1,{{\left{ p \right}}_b}} \right)}\quad (m\in \N,p>1) ] are reducible to polynomials in zeta values, and give explicit recurrence formulas. Some interesting (known or new) consequences and illustrative examples are considered.

Summary

We haven't generated a summary for this paper yet.