Results 1 to 10 of about 23,383 (119)

Median Bernoulli Numbers and Ramanujan’s Harmonic Number Expansion

Mathematics, 2022
Ramanujan-type harmonic number expansion was given by many authors. Some of the most well-known are: Hn∼γ+logn−∑k=1∞Bkk·nk, where Bk is the Bernoulli numbers.
Kwang-Wu Chen
doaj   +1 more source

Probabilistic Interpretation of Number Operator Acting on Bernoulli Functionals

Mathematics, 2022
Let N be the number operator in the space H of real-valued square-integrable Bernoulli functionals. In this paper, we further pursue properties of N from a probabilistic perspective.
Jing Zhang, Lixia Zhang, Caishi Wang
doaj   +1 more source

Two identities and closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind

Demonstratio Mathematica, 2022
In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan, Wu Lan, Lim Dongkyu, Qi Feng   +3 more
doaj   +1 more source

On a more accurate half-discrete Hilbert-type inequality involving hyperbolic functions

Open Mathematics, 2022
In this work, by the introduction of a new kernel function composed of exponent functions with several parameters, and using the method of weight coefficient, Hermite-Hadamard’s inequality, and some other techniques of real analysis, a more accurate half-
You Minghui, Sun Xia, Fan Xiansheng
doaj   +1 more source

On a new generalization of some Hilbert-type inequalities

Open Mathematics, 2021
In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established.
You Minghui, Song Wei, Wang Xiaoyu
doaj   +1 more source

Sums involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
We offer a number of various finite and infinite sum identities involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers. For example, among many others, we prove Σⁿₖ₌ₒ((-1)ᵏhₖ/4ᵏ)$binom{2k}{k}$Gₙ₋ₖ = ((-1)ⁿ⁻¹/2^²ⁿ⁻¹)
Necdet Batır, Anthony Sofo
doaj   +1 more source

Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function

Advances in Difference Equations, 2021
A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function.
Taekyun Kim, Dae San Kim, Lee-Chae Jang, Hyunseok Lee, Hanyoung Kim   +4 more
doaj   +1 more source

Fungsi Zeta Riemann Genap Menggunakan Bilangan Bernoulli

Desimal, 2019
In this article, we study about the value of Riemann Zeta Function for even numbers using Bernoulli number. First, we give some basic theory about Bernoulli number and Riemann Zeta function.
Ikhsan Maulidi, Vina Apriliani, Muhamad Syazali   +2 more
doaj   +1 more source

Various Structures of the Roots and Explicit Properties of q-cosine Bernoulli Polynomials and q-sine Bernoulli Polynomials

Mathematics, 2020
In this paper, we define cosine Bernoulli polynomials and sine Bernoulli polynomials related to the q-number. Furthermore, we intend to find the properties of these polynomials and check the structure of the roots.
Jung Yoog Kang, Chen Seoung Ryoo
doaj   +1 more source

Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials

Mathematics, 2016
In the paper, the authors recall some known determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, find alternative determinantal expressions in terms of the Hessenberg determinants for the Bernoulli ...
Feng Qi, Bai-Ni Guo
doaj   +1 more source