Results 11 to 20 of about 46,762 (263)
Binomial Sum Relations Involving Fibonacci and Lucas Numbers
AppliedMath, 2023 In this paper, we provide a first systematic treatment of binomial sum relations involving (generalized) Fibonacci and Lucas numbers. The paper introduces various classes of relations involving (generalized) Fibonacci and Lucas numbers and different ...
Kunle Adegoke +2 more
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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
Γmer Eugeciouglu +2 more
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Fractional Sums and Differences with Binomial Coefficients
Discrete Dynamics in Nature and Society, 2013 In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives.
Thabet Abdeljawad +3 more
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Euler-type sums involving multiple harmonic sums and binomial coefficients
Open Mathematics, 2021 In this paper, we mainly show that generalized Euler-type sums of multiple harmonic sums with reciprocal binomial coefficients can be expressed in terms of rational linear combinations of products of classical multiple zeta values (MZVs) and multiple ...
Si Xin
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A sum of binomial coefficients [PDF]
Mathematics of Computation, 1978 An explicit expression is derived for the sum of the ( k + 1 ) (k + 1) st binomial coefficients in the nth, ( n β m ) (n - m) th, ( n β 2 m ) (n - 2m) th,... row of the arithmetic triangle.
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Infinite series containing quotients of central binomial coefficients [PDF]
Notes on Number Theory and Discrete MathematicsBy making use of the Wallis' integral formulae and integration by parts, two classes of infinite series are evaluated, in closed form, in terms of Ο and Riemann zeta function.
Zhiling Fan
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Sums of Reciprocals of Triple Binomial Coefficients
International Journal of Mathematics and Mathematical Sciences, 2008 We investigate the integral representation of infinite sums involving the reciprocals of triple binomial coefficients. We also recover some wellknown properties of π(3) and extend the range of results given by other authors.
A. Sofo
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On some series involving the binomial coefficients $binom{3n}{n}$ [PDF]
Notes on Number Theory and Discrete MathematicsUsing a simple transformation, we obtain much simpler forms for some series involving binomial coefficients $binom{3n}{n}$ derived by Necdet Batir. New evaluations are given and connections with Fibonacci numbers and the golden ratio are established ...
Kunle Adegoke +2 more
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Some combinatorial identities containing central binomial coefficients or Catalan numbers*
Applied Mathematics in Science and Engineering, 2023 In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four ...
Feng Qi, Da-Wei Niu, Dongkyu Lim
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On the divisibility of binomial coefficients
Ars Mathematica Contemporanea, 2020 In Pacific J. Math. 292 (2018), 223-238, Shareshian and Woodroofe asked if for every positive integer $n$ there exist primes $p$ and $q$ such that, for all integers $k$ with $1 \leq k \leq n-1$, the binomial coefficient $\binom{n}{k}$ is divisible by at least one of $p$ or $q$. We give conditions under which a number $n$ has this property and discuss a
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