Results 21 to 30 of about 178,978 (284)
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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A Fast Algorithm for Computing Binomial Coefficients Modulo Powers of Two
The Scientific World Journal, 2013 I present a new algorithm for computing binomial coefficients modulo . The proposed method has an preprocessing time, after which a binomial coefficient with can be computed modulo in time.
Mugurel Ionut Andreica
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Series of Convergence Rate −1/4 Containing Harmonic Numbers
Axioms, 2023 Two general transformations for hypergeometric series are examined by means of the coefficient extraction method. Several interesting closed formulae are shown for infinite series containing harmonic numbers and binomial/multinomial coefficients.
Chunli Li, Wenchang Chu
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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. Also, the computational science is a rapidly growing interdisciplinary area where science, computation, mathematics, and its collaboration use advanced computing ...
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Bisecting binomial coefficients
Discrete Applied Mathematics, 2017 In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously unknown) infinite classes of integers which admit nontrivial bisections, and a class with only trivial bisections. As a byproduct of this last construction, we show conjectures Q2 and Q4 of Cusick and Li.
Eugen J. Ionaşcu +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
Ömer Eugeciouglu +2 more
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Some congruences involving binomial coefficients
, 2015 Binomial coefficients and central trinomial coefficients play important roles in combinatorics. Let $p>3$ be a prime. We show that $$T_{p-1}\equiv\left(\frac p3\right)3^{p-1}\ \pmod{p^2},$$ where the central trinomial coefficient $T_n$ is the constant ...
Cao, Hui-Qin, Sun, Zhi-Wei
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Molecular Oncology, EarlyView.To integrate multiple transcriptomics data with severe batch effects for identifying MB subtypes, we developed a novel and accurate computational method named RaMBat, which leveraged subtype‐specific gene expression ranking information instead of absolute gene expression levels to address batch effects of diverse data sources.
Mengtao Sun, Jieqiong Wang, Shibiao Wan
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AppliedMathBased on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived.
Kunle Adegoke, Robert Frontczak
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Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model
Comptes Rendus. Mathématique, 2023 In categorical data analysis, the $2\times 2$ contingency tables are commonly used to assess the association between groups and responses, this is achieved by using some measures of association, such as the contingency coefficient, odds ratio, risk ...
Andrade, Jose A. A., Rathie, Pushpa
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