Results 21 to 30 of about 54,043 (268)

Inequalities for Binomial Coefficients

Journal of Mathematical Analysis and Applications, 1999
For any real number \(r\) with \(r>1\), let \(c_r= (2\pi(1-{1\over r}))^{-1/2}\) and \(d_r= (r-1)/(1-{1\over r})^r\). Let \(B_{2m}\) \((m= 1,2,\dots)\) be the Bernoulli numbers defined by \[ {z\over e^z-1}=1-{z\over 2}+\sum^\infty_{m=1} B_{2m}{z^{2m}\over (2m)!}.
openaire   +2 more sources

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

A generalization of the binomial coefficients

Discrete Mathematics, 1992
We pose the question of what is the best generalization of the factorial and the binomial coefficient. We give several examples, derive their combinatorial properties, and demonstrate their interrelationships. On cherche ici à déterminer est la meilleure généralisation possible des factorielles et des coefficients du binôome. On s'interesse à plusieurs
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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, Timothy Redmond, Charles Ryavec   +2 more
doaj   +1 more source

On sums of binomial coefficients [PDF]

Proyecciones (Antofagasta)
We investigate the integral representation of infinite sums involving the ratio of binomial coefficients. We also recover some wellknown properties of ζ (3) and extend the range of results given by other authors. 
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New Harmonic Number Series

AppliedMath
Based 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

High‐Resolution MRI Revealed Different Etiology‐Specific Associations With Cerebral Infarction in Adult Moyamoya Vasculopathy

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective High‐resolution MRI enables detailed assessment of intracranial vessel wall pathology in moyamoya vasculopathy. We aimed to classify adult moyamoya vasculopathy etiologies using high‐resolution MRI and to examine subtype‐specific associations between high‐resolution MRI features and ischemic infarction.
Guangsong Han, Jiachun Pan, Yuehui Hong, Xiaoyuan Fan, Ming Yao, Lixin Zhou, Yicheng Zhu, Feng Feng, Jun Ni   +8 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

Mycophenolate Mofetil Treatment Reduces the Risk of Treatment Escalation Due to Vascular Complications in Limited Cutaneous Systemic Sclerosis: Emulation of a Target Trial From the Italian Rheumatology Society SPRING Registry

Arthritis Care &Research, EarlyView.
Objective Mycophenolate mofetil (MMF) use in limited cutaneous systemic sclerosis (lcSSc) is relatively uncommon because of the lower fibrotic burden and the predominance of vascular complications. In vitro observations and clinical data from transplanted patients suggest a protective effect of MMF on endothelial function.
Enrico De Lorenzis, Gerlando Natalello, Rossella De Angelis, Lucrezia Verardi, Dilia Giuggioli, Gianluigi Bajocchi, Lorenzo Dagna, Silvia Bellando‐Randone, Giovanni Zanframundo, Rosario Foti, Fabio Cacciapaglia, Giovanna Cuomo, Alarico Ariani, Edoardo Rosato, Gemma Lepri, Francesco Girelli, Valeria Riccieri, Elisabetta Zanatta, Ilaria Cavazzana, Francesca Ingegnoli, Maria De Santis, Giuseppe Murdaca, Giuseppina Abignano, Giorgio Pettiti, Alessandra Della Rossa, Maurizio Caminiti, Annamaria Iuliano, Giovanni Ciano, Lorenzo Beretta, Gianluca Bagnato, Ennio Lubrano, Maria Ilenia De Andres, Alessandro Giollo, Cosimo Bruni, Martina Orlandi, Marco Fornaro, Marta Saracco, Cecilia Agnes, Pier Giacomo Cerasuolo, Gabriella Alonzi, Edoardo Cipolletta, Federica Lumetti, Amelia Spinella, Luca Magnani, Corrado Campochiaro, Giacomo De Luca, Veronica Codullo, Elisa Visalli, Carlo Iandoli, Antonietta Gigante, Greta Pellegrino, Erika Pigatto, Maria‐Grazia Lazzaroni, Franco Franceschini, Elena Generali, Gianna Mennillo, Simone Barsotti, Giuseppa Pagano Mariano, Federica Furini, Licia Vultaggio, Simone Parisi, Clara Lisa Peroni, Gerolamo Bianchi, Enrico Fusaro, Gian Domenico Sebastiani, Marcello Govoni, Salvatore D'Angelo, Franco Cozzi, Fabrizio Conti, Serena Guiducci, Andrea Doria, Carlo Salvarani, Florenzo Iannone, Maria Antonietta D'Agostino, Clodoveo Ferri, Marco Matucci Cerinic, Silvia Laura Bosello, on behalf of the SPRING Italian Registry Collaborators   +77 more
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Characteristic polynomials of some min and max matrices

Mathematics Open
In this paper, we investigate Min matrices [Formula: see text] and Max matrices [Formula: see text] whose entries are [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] and [Formula: see text]. By utilizing combinatorial
Wei Xie
doaj   +1 more source