Results 21 to 30 of about 46,123 (300)
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 +2 more
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Novel Binomial Series without Binomial Coefficients
, 2023 Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical equations for solving today’s scientific problems and challenges. For this purpose, a novel binomial series (new binomial theorem) without
Chinnaraji Annamalai
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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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ON DIVISIBILITY OF BINOMIAL COEFFICIENTS [PDF]
Journal of the Australian Mathematical Society, 2012 AbstractIn this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.
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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 π and Riemann zeta function.
Zhiling Fan
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Poset binomials and rainbow characters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 This paper introduces a variation on the binomial coefficient that depends on a poset and interpolates between $q$-binomials and 1-binomials: a total order gives the usual $q$-binomial, and a poset with no relations gives the usual binomial coefficient ...
Daniel Bragg, Nathaniel Thiem
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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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On Binomial Coefficient Residues [PDF]
Canadian Journal of Mathematics, 1957 The number of binomial coefficients , which are congruent to j , 0 ≤ j ≤ p − 1, modulo the prime number p is denoted by θj(n). In this paper we give systems of simultaneous linear difference equations with constant coefficients whose
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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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