Results 201 to 210 of about 21,447 (236)

Volume and Structure of Maxillofacial Trauma Before, During, and After COVID-19 Restrictions: A Multicentre Interrupted Time-Series and Period-Comparative Analysis of 3954 Patients. [PDF]

Medicina (Kaunas)
Czako L, Janickova M, Borza B, Kalmanova S, Juricek R, Sovis M, Kobyliakova A, Kizek P.   +7 more
europepmc   +1 more source

Finite Sums Involving Reciprocals of the Binomial and Central Binomial Coefficients and Harmonic Numbers [PDF]

Symmetry, 2021
We prove some finite sum identities involving reciprocals of the binomial and central binomial coefficients, as well as harmonic, Fibonacci and Lucas numbers, some of which recover previously known results, while the others are new.
Anthony Sofo, Necdet BATIR
exaly   +3 more sources

Factors of certain sums involving central q-binomial coefficients [PDF]

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2021
Recently, Ni and Pan proved a $q$-congruence on certain sums involving central $q$-binomial coefficients, which was conjectured by Guo. In this paper, we give a generalization of this $q$-congruence and confirm another $q$-congruence, also conjectured by Guo.
Victor J. W. Guo
exaly   +4 more sources

More congruences for central binomial coefficients

Journal of Number Theory, 2010
Let \(p>5\) be a prime number. The author proves that \[ \sum_{k=1}^{p-1}\frac{1}{k^2}\binom{2k}{k}^{-1}\equiv\frac13 \frac{H(1)}{p}\pmod {p^3} \] and that \[ \sum_{k=1}^{p-1}\frac{(-1)^k}{k^3}\binom{2k}{k}^{-1}\equiv-\frac25 \frac{H(1)}{p^2}\pmod {p^3}, \] where \(H(1)=\sum_{k=1}^{p-1}\frac{1}{k}\).
Roberto Tauraso
exaly   +4 more sources

On congruences related to central binomial coefficients

Journal of Number Theory, 2011
It is known that $\sum_{k=0}^\infty\binom{2k}{k}/((2k+1)4^k)=π/2$ and $\sum_{k=0}^\infty\binom{2k}{k}/((2k+1)16^k)=π/3$. In this paper we obtain their p-adic analogues such as $$\sum_{p/23 is a prime and E_0,E_1,E_2,... are Euler numbers. Besides these, we also deduce some other congruences related to central binomial coefficients. In addition, we pose
Sun Zhiwei
exaly   +3 more sources

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

Journal of Difference Equations and Applications, 2022
Necdet BATIR, Kwang-Wu Chen
exaly   +2 more sources

The Series of Reciprocals of Non-central Binomial Coefficients ()

American Journal of Computational Mathematics, 2013
Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients.
Laiping Zhang, Wanhui Ji
exaly   +3 more sources

Wallis's Product and the Central Binomial Coefficient

The American Mathematical Monthly, 2015
(2015). Wallis's Product and the Central Binomial Coefficient. The American Mathematical Monthly: Vol. 122, No. 7, pp. 689-689.
openaire   +1 more source

Central and local limit theorems for the coefficients of polynomials of binomial type

Journal of Combinatorial Theory - Series A, 1977
AbstractWe introduce the problem of establishing a central limit theorem for the coefficients of a sequence of polynomials Pn(x) of binomial type; that is, a sequence Pn(x) satisfying exp(xg(u)) = ∑n=0∞ Pn(x)(unn!) for some (formal) power series g(u) lacking constant term.
E Rodney Canfield
exaly   +4 more sources