Results 21 to 30 of about 21,447 (236)

Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]

Notes on Number Theory and Discrete Mathematics
We find various series that involve the central binomial coefficients $binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function _pF_q approach, our method utilizes a straightforward transformation to ...
Segun Olofin Akerele, Olamide Esther Salami   +1 more
doaj   +1 more source

On certain congruences involving central binomial coefficients

Mathematica Montisnigri, 2023
Let p be an odd prime. In this paper, using some properties of Fibonacci numbers, reciprocal polynomials for Fibonacci polynomials, and Legendre symbol, we establish some congruences involving central binomial coefficient modulo p and p^2. We also give some new identities for hyperbolic functions.
Rachid Boumahdi, Miloud Mihoubi, Laala Khaldi   +2 more
openaire   +1 more source

Powers in Prime Bases and a Problem on Central Binomial Coefficients

Integers, 2015
12 ...
Holdum, Sebastian Tim, Klausen, Frederik Ravn, Rasmussen, Peter Michael Reichstein   +2 more
openaire   +4 more sources

Some congruences involving central q-binomial coefficients

Advances in Applied Mathematics, 2010
16 pages, detailed proofs of Theorems 4.1 and 4.3 are added, to appear in Adv.
Victor J. W. Guo, Jiang Zeng
openaire   +3 more sources

Relationship Between Neurologic Symptoms and Signs and FMR1 Genotype in Premutation Carriers

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Background and Objectives Fragile X‐associated Tremor/Ataxia Syndrome (FXTAS) is the most severe late‐onset condition caused by a premutation in the FMR1 gene, characterized by expanded CGG triplet repeats of 55–200. Clinical presentations of FXTAS, including gait ataxia, kinetic tremor, cognitive decline, and rare Parkinsonism, are linked to ...
Flora Tassone, Freddy Chafota, Miguel E. Rentería, Randi J. Hagerman, Ellery Santos, Anna Atkinson, Nicholas G. Martin, Elsdon Storey, Danuta Z. Loesch   +8 more
wiley   +1 more source

Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients

Axioms
We examine a useful hypergeometric transformation formula by means of the coefficient extraction method. A large class of “binomial/harmonic series” (of convergence ratio “1/4”) containing the cubic central binomial coefficients and harmonic numbers is ...
Chunli Li, Wenchang Chu
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

Parametric Integrals for Binomial Series with Harmonic Polynomials

Axioms
Binomial series involving harmonic polynomials are expressed in terms of parametric integrals. By evaluating these parametric integrals, we establish several remarkable closed formulae for the infinite series containing both central binomial coefficients
Chunli Li, Wenchang Chu
doaj   +1 more source

Reserves, Injury Severity, and Outcomes in Traumatic Brain Injury: A CENTER‐TBI Observational Study

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Reserve refers to the brain's ability to maintain function after an injury and strongly relates to traumatic brain injury (TBI) outcomes. This study examined (1) whether associations between pre‐injury reserve proxies and outcomes differed across injury severity categories, and (2) whether the impact of injury severity varied across ...
Natascha Ekdahl, Marika C. Möller, Lindsay Wilson, Anne Vik, Toril Skandsen, Jonas Stenberg, CENTER‐TBI participants and investigators   +6 more
wiley   +1 more source

Association Between Neurofilament Light Chain and Real‐World Ambulatory Function in Progressive MS

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Neurofilament light chain (NfL) is a biomarker of neuroaxonal injury in multiple sclerosis (MS), yet associations with functional outcomes remain unclear. Longitudinal associations between serum NfL (sNfL) and daily step count (STEPS) from wearable devices were assessed in a large international progressive MS cohort.
Gabby B. Joseph, Megan McCune, Riley Bove, Ahmed Abdelhak, Bruce A. C. Cree, Valerie J. Block   +5 more
wiley   +1 more source