Results 21 to 30 of about 180,364 (280)
Series of Convergence Rate −1/4 Containing Harmonic Numbers
Axioms, 2023 Two general transformations for hypergeometric series are examined by means of the coefficient extraction method. Several interesting closed formulae are shown for infinite series containing harmonic numbers and binomial/multinomial coefficients.
Chunli Li, Wenchang Chu
doaj +1 more source
Binomial Series without Binomial Coefficients
, 2023 Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical equations for solving today’s scientific problems and challenges. Also, the computational science is a rapidly growing interdisciplinary area where science, computation, mathematics, and its collaboration use advanced computing ...
openaire +1 more source
Bisecting binomial coefficients
Discrete Applied Mathematics, 2017 In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously unknown) infinite classes of integers which admit nontrivial bisections, and a class with only trivial bisections. As a byproduct of this last construction, we show conjectures Q2 and Q4 of Cusick and Li.
Eugen J. Ionaşcu +2 more
openaire +3 more sources
Evaluation of a Special Hankel Determinant of Binomial Coefficients [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 This paper makes use of the recently introduced technique of $\gamma$-operators to evaluate the Hankel determinant with binomial coefficient entries $a_k = (3 k)! / (2k)! k!$. We actually evaluate the determinant of a class of polynomials $a_k(x)$ having
Ömer Eugeciouglu +2 more
doaj +1 more source
On the least common multiple of $q$-binomial coefficients
, 2009 In this paper, we prove the following identity $$ \lcm({n\brack 0}_q,{n\brack 1}_q,...,{n\brack n}_q) =\frac{\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q}, $$ where ${n\brack k}_q$ denotes the $q$-binomial coefficient and $[n]_q=\frac{1-q^n}{1-q}$. This result
Farhi B. +5 more
core +1 more source
AppliedMathBased on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived.
Kunle Adegoke, Robert Frontczak
doaj +1 more source
Weighted Lattice Paths Enumeration by Gaussian Polynomials
, 2017 The Gaussian polynomial in variable $q$ is defined as the $q$-analog of the binomial coefficient. In addition to remarkable implications of these polynomials to abstract algebra, matrix theory and quantum computing, there is also a combinatorial ...
Martinjak, Ivica, Zubac, Ivana
core +1 more source
Shared Genetic Effects and Antagonistic Pleiotropy Between Multiple Sclerosis and Common Cancers
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Epidemiologic studies have reported inconsistent altered cancer risk in individuals with multiple sclerosis (MS). Factors such as immune dysregulation, comorbidities, and disease‐modifying therapies may contribute to this variability.
Asli Buyukkurt +5 more
wiley +1 more source
Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model
Comptes Rendus. Mathématique, 2023 In categorical data analysis, the $2\times 2$ contingency tables are commonly used to assess the association between groups and responses, this is achieved by using some measures of association, such as the contingency coefficient, odds ratio, risk ...
Andrade, Jose A. A., Rathie, Pushpa
doaj +1 more source
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Glioma recurrence severely impacts patient prognosis, with current treatments showing limited efficacy. Traditional methods struggle to analyze recurrence mechanisms due to challenges in assessing tumor heterogeneity, spatial dynamics, and gene networks.
Lei Qiu +10 more
wiley +1 more source