New Identities Involving Cauchy Numbers, Harmonic Numbers and Zeta Values

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Marc-Antoine Coppo
Keyword(s):  
Harmonic Numbers ◽  
Cauchy Numbers ◽  
Zeta Values

scholarly journals A new class of identities involving Cauchy numbers, harmonic numbers and zeta values

2012 ◽  
Vol 27 (3) ◽  
pp. 305-328 ◽  
Author(s):  
Bernard Candelpergher ◽  
Marc-Antoine Coppo
Keyword(s):  
Harmonic Numbers ◽  
New Class ◽  
Cauchy Numbers ◽  
Zeta Values

scholarly journals A note on harmonic number identities, Stirling series and multiple zeta values

2019 ◽  
Vol 15 (07) ◽  
pp. 1323-1348
Author(s):  
Markus Kuba ◽  
Alois Panholzer
Keyword(s):  
Infinite Series ◽  
General Type ◽  
Multiple Zeta Values ◽  
Harmonic Numbers ◽  
Special Values ◽  
Multiple Zeta ◽  
Special Cases ◽  
Zeta Values ◽  
Finite Sums ◽  
Binomial Sums

We study a general type of series and relate special cases of it to Stirling series, infinite series discussed by Choi and Hoffman, and also to special values of the Arakawa–Kaneko zeta function, studied before amongst others by Candelpergher and Coppo, and also by Young. We complement and generalize earlier results. Moreover, we survey properties of certain truncated multiple zeta and zeta star values, pointing out their relation to finite sums of harmonic numbers. We also discuss the duality result of Hoffman, relating binomial sums and truncated multiple zeta star values.

Generalized harmonic numbers and Euler sums

2017 ◽  
Vol 13 (02) ◽  
pp. 513-528 ◽  
Author(s):  
Kwang-Wu Chen
Keyword(s):  
Zeta Functions ◽  
Multiple Zeta Values ◽  
Harmonic Numbers ◽  
Special Values ◽  
Euler Sums ◽  
Summation Formulas ◽  
Multiple Zeta ◽  
Zeta Values ◽  
New Formula ◽  
Generalized Harmonic Numbers

In this paper, we investigate two kinds of Euler sums that involve the generalized harmonic numbers with arbitrary depth. These sums establish numerous summation formulas including the special values of Arakawa–Kaneno zeta functions and a new formula of multiple zeta values of height one as examples.

scholarly journals Generalized Hyperharmonic Number Sums With Reciprocal Binomial Coefficients

2021 ◽  
Author(s):  
Rusen Li
Keyword(s):  
Binomial Coefficients ◽  
Harmonic Numbers ◽  
Euler Sums ◽  
Zeta Values

In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.

scholarly journals Combinatorial Identities with Generalized Higher-order Genocchi Sequences

2019 ◽  
Vol 12 (2) ◽  
pp. 605-621
Author(s):  
Tian Hao ◽  
Wuyungaowa Bao
Keyword(s):  
Probabilistic Method ◽  
Fibonacci Numbers ◽  
Stirling Numbers ◽  
Higher Order ◽  
Harmonic Numbers ◽  
Bell Numbers ◽  
Genocchi Numbers ◽  
Genocchi Polynomials ◽  
Cauchy Numbers ◽  
The Moment

In this paper, we make use of the probabilistic method to calculate the moment representation of generalized higher-order Genocchi polynomials. We obtain the moment expression of the generalized higher-order Genocchi numbers with a and b parameters. Some characteriza tions and identities of generalized higher-order Genocchi polynomials are given by the proof of the moment expression. As far as properties given by predecessors are concerned, we prove them by the probabilistic method. Finally, new identities of relationships involving generalized higher-order Genocchi numbers and harmonic numbers, derangement numbers, Fibonacci numbers, Bell numbers, Bernoulli numbers, Euler numbers, Cauchy numbers and Stirling numbers of the second kind are established. 

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

scholarly journals ON MULTIPLE ZETA VALUES OF EXTREMAL HEIGHT

2015 ◽  
Vol 93 (2) ◽  
pp. 186-193 ◽  
Author(s):  
MASANOBU KANEKO ◽  
MIKA SAKATA
Keyword(s):  
Explicit Formula ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Maximal Height ◽  
Zeta Values ◽  
Sum Formula

We give three identities involving multiple zeta values of height one and of maximal height: an explicit formula for the height-one multiple zeta values, a regularised sum formula and a sum formula for the multiple zeta values of maximal height.

Sign in / Sign up

Export Citation Format

Share Document