On generating functions of multiple zeta values and generalized hypergeometric functions

2010 ◽  
Vol 134 (1-2) ◽  
pp. 139-155 ◽  
Author(s):  
Takashi Aoki ◽  
Yasuo Ohno ◽  
Noriko Wakabayashi
Keyword(s):  
Generating Functions ◽  
Hypergeometric Functions ◽  
Multiple Zeta Values ◽  
Generalized Hypergeometric Functions ◽  
Multiple Zeta ◽  
Zeta Values

scholarly journals Some relations of interpolated multiple zeta values

2017 ◽  
Vol 28 (05) ◽  
pp. 1750033 ◽  
Author(s):  
Zhonghua Li ◽  
Chen Qin
Keyword(s):  
Generating Function ◽  
Hypergeometric Functions ◽  
Multiple Zeta Values ◽  
Fixed Weight ◽  
Multiple Zeta ◽  
Special Cases ◽  
Zeta Values

In this paper, the extended double shuffle relations for interpolated multiple zeta values (MZVs) are established. As an application, Hoffman’s relations for interpolated MZVs are proved. Furthermore, a generating function for sums of interpolated MZVs of fixed weight, depth and height is represented by hypergeometric functions, and we discuss some special cases.

scholarly journals On multiple zeta values of even arguments

2017 ◽  
Vol 13 (03) ◽  
pp. 705-716 ◽  
Author(s):  
Michael E. Hoffman
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Generating Functions ◽  
Bernoulli Number ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
The Riemann Zeta Function ◽  
Zeta Values ◽  
Riemann Zeta

For [Formula: see text], let [Formula: see text] be the sum of all multiple zeta values with even arguments whose weight is [Formula: see text] and whose depth is [Formula: see text]. Of course [Formula: see text] is the value [Formula: see text] of the Riemann zeta function at [Formula: see text], and it is well known that [Formula: see text]. Recently Shen and Cai gave formulas for [Formula: see text] and [Formula: see text] in terms of [Formula: see text] and [Formula: see text]. We give two formulas for [Formula: see text], both valid for arbitrary [Formula: see text], one of which generalizes the Shen–Cai results; by comparing the two we obtain a Bernoulli-number identity. We also give explicit generating functions for the numbers [Formula: see text] and for the analogous numbers [Formula: see text] defined using multiple zeta-star values of even arguments.

Zeta Mahler measures, multiple zeta values and L-values

2015 ◽  
Vol 11 (07) ◽  
pp. 2239-2246
Author(s):  
Yoshitaka Sasaki
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Mahler Measure ◽  
Multiple Zeta Values ◽  
Explicit Formulas ◽  
Multiple Zeta ◽  
Zeta Values

The zeta Mahler measure is the generating function of higher Mahler measures. In this article, explicit formulas of higher Mahler measures, and relations between higher Mahler measures and multiple zeta (star) values are showed by observing connections between zeta Mahler measures and the generating functions of multiple zeta (star) values. Additionally, connections between higher Mahler measures and Dirichlet L-values associated with primitive quadratic characters are discussed.

scholarly journals Some Weighted Sum Formulas for Multiple Zeta, Hurwitz Zeta, and Alternating Multiple Zeta Values

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Yuan He ◽  
Zhuoyu Chen
Keyword(s):  
Generating Functions ◽  
Weighted Sums ◽  
Weighted Sum ◽  
Trigonometric Functions ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Euler Polynomials And Numbers ◽  
Zeta Values

We perform a further investigation for the multiple zeta values and their variations and generalizations in this paper. By making use of the method of the generating functions and some connections between the higher-order trigonometric functions and the Lerch zeta function, we explicitly evaluate some weighted sums of the multiple zeta, Hurwitz zeta, and alternating multiple zeta values in terms of the Bernoulli and Euler polynomials and numbers. It turns out that various known results are deduced as special cases.

Motivic multiple zeta values relative to μ2

2020 ◽  
Vol 14 (10) ◽  
pp. 2685-2712
Author(s):  
Zhongyu Jin ◽  
Jiangtao Li
Keyword(s):  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values
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