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.

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.

Finite Mixed Sums wih Harmonic Terms

2015 ◽  
Vol 65 (5) ◽  
Author(s):  
Anthony Sofo
Keyword(s):  
Higher Order ◽  
Binomial Coefficients ◽  
Harmonic Numbers ◽  
Euler Sums ◽  
Finite Sums ◽  
Sums Of Products

AbstractIn the spirit of Euler sums we develop a set of identities for finite sums of products of harmonic numbers in higher order and reciprocal binomial coefficients. The new results complement some Euler sums of the type

scholarly journals Harmonic Numbers and Cubed Binomial Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Anthony Sofo
Keyword(s):  
Closed Form ◽  
Binomial Coefficients ◽  
Harmonic Numbers ◽  
Polygamma Functions ◽  
Form Representation ◽  
The Given

Euler related results on the sum of the ratio of harmonic numbers and cubed binomial coefficients are investigated in this paper. Integral and closed-form representation of sums are developed in terms of zeta and polygamma functions. The given representations are new.

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 Congruences involving alternating sums related to harmonic numbers and binomial coefficients

2020 ◽  
Vol 26 (4) ◽  
pp. 39-51
Author(s):  
Laid Elkhiri ◽  
◽  
Miloud Mihoubi ◽  
Abdellah Derbal ◽  
◽  
...  
Keyword(s):  
Prime Number ◽  
Binomial Coefficients ◽  
Harmonic Numbers ◽  
Arithmetic Properties ◽  
Alternating Sums ◽  
Generalized Harmonic Numbers

In 2017, Bing He investigated arithmetic properties to obtain various basic congruences modulo a prime for several alternating sums involving harmonic numbers and binomial coefficients. In this paper we study how we can obtain more congruences modulo a power of a prime number p (super congruences) in the ring of p-integer \mathbb{Z}_{p} involving binomial coefficients and generalized harmonic numbers.

scholarly journals Supercongruences related to 3F2(1) involving harmonic numbers

2018 ◽  
Vol 14 (04) ◽  
pp. 1093-1109 ◽  
Author(s):  
Roberto Tauraso
Keyword(s):  
Infinite Series ◽  
Binomial Coefficients ◽  
Harmonic Numbers

We provide various supercongruences for truncated series which involve central binomial coefficients and harmonic numbers. The corresponding infinite series are also evaluated.

Identities for the harmonic numbers and binomial coefficients

2010 ◽  
Vol 25 (1) ◽  
pp. 93-113 ◽  
Author(s):  
Anthony Sofo ◽  
H. M. Srivastava
Keyword(s):  
Binomial Coefficients ◽  
Harmonic Numbers
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