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Spatiotemporal Trends and Co-Resistance Patterns of Multidrug-Resistant Enteric <i>Escherichia coli</i> O157 Infections in Humans in the United States. [PDF]

Pathogens
Bhatt T, Varga C.
europepmc   +1 more source

Comparison of statistical methods for the analysis of patient-reported outcomes (PROs), particularly the Short-Form 36 (SF-36), in randomised controlled trials (RCTs) using standardised effect size (SES): an empirical analysis. [PDF]

Health Qual Life Outcomes
Qian Y, Walters SJ, Jacques RM, Flight L.   +3 more
europepmc   +1 more source

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Solution to a problem involving central binomial coefficients

Integral Transforms and Special Functions
In this paper, we solve an open problem considered by Steven Finch (Central Binomial Coefficients, 2007, Available from: http://www.people.fas.harvard.edu/sfinch/csolve/cbc.pdf, p. 5), as far back as 2007, concerning the calculation of a series involving
Nandan Sai Dasireddy
semanticscholar   +4 more sources

Combinatorial identities involving reciprocals of the binomial and central binomial coefficients and harmonic numbers

Journal of Difference Equations and Applications, 2022
We prove a general combinatorial formula involving the reciprocals of the binomial coefficients and the partial sum of an arbitrary sequence. Applying this formula we offer many combinatorial identities involving reciprocals of the binomial and central ...
Necdet Batır, Kwang-Wu Chen
semanticscholar   +3 more sources

INFINITE SERIES CONCERNING HARMONIC NUMBERS AND QUINTIC CENTRAL BINOMIAL COEFFICIENTS

Bulletin of the Australian Mathematical Society, 2023
By examining two hypergeometric series transformations, we establish several remarkable infinite series identities involving harmonic numbers and quintic central binomial coefficients, including five conjectured recently by Z.-W.
Chunli Li, W. Chu
semanticscholar   +3 more sources

PROOF OF TWO CONJECTURES ON SUPERCONGRUENCES INVOLVING CENTRAL BINOMIAL COEFFICIENTS

Bulletin of the Australian Mathematical Society, 2020
In this note we use some q-congruences proved by the method of ‘creative microscoping’ to prove two conjectures on supercongruences involving central binomial coefficients. For instance, we confirm the m = 5 case of Conjecture 1.1 in [Integral Transforms
CHENG-YANG Gu, Victor J. W. Guo
semanticscholar   +3 more sources

ON SOME CONGRUENCES INVOLVING CENTRAL BINOMIAL COEFFICIENTS

Bulletin of the Australian Mathematical Society
AbstractWe prove the following conjecture of Z.-W. Sun [‘On congruences related to central binomial coefficients’, J. Number Theory13(11) (2011), 2219–2238]. Let p be an odd prime. Then $$ \begin{align*} \sum_{k=1}^{p-1}\frac{\binom{2k}k}{k2^k}\equiv-\frac12H_{{(p-1)}/2}+\frac7{16}p^2B_{p-3}\pmod{p^3}, \end{align*} $$ where $H_n$ is the nth harmonic
Guo-Shuai Mao
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Summation Formulas on Harmonic Numbers and Five Central Binomial Coefficients

Mathematical Notes, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chunli Li, Wenchang Chu
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The inverse versine function and sums containing reciprocal central binomial coefficients and reciprocal Catalan numbers

International Journal of Mathematical Education in Science and Technology, 2021
Using the inverse of the once common but now largely forgotten versine function, series containing reciprocals of the central binomial coefficients and series containing reciprocals of the Catalan numbers are explored.
S. Stewart
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Series Involving Cubic Central Binomial Coefficients of Convergence Rate 1/64

Bulletin of the Malaysian Mathematical Sciences Society
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Chunli Li, Wenchang Chu
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